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Table showing the aRT in number of function evaluations divided by the best aRT measured during BBOB-2009

Last dimension | Dimension = 2 | Next dimension

Δ fopt
f1, 2-D
1e1
2.0
1e0
6.0
1e-1
6.0
1e-2
6.0
1e-3
6.0
1e-5
6.0
1e-7
6.0
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.1 (2)2.7 (1)3.8 (0.6)6.1 (0)6.7 (0.2)8.8 (0.8)11 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 4.6 (3)4.0 (2)8.1 (5)11 (1)14 (2)17 (0.5)20 (2)15/15
CGA-grid100 holtschulte noiseless 2.1 (1)3.3 (2)59 (52)242 (255)854 (945)4905 (2812)4.5e4 (7e4)1/15
CGA-grid16 holtschulte noiseless 1.6 (1)9.0 (10)29 (17)65 (44)215 (138)1271 (886)1.4e4 (1e4)3/15
CGA-ring100 holtschulte noiseless 2.0 (2)5.9 (4)26 (13)139 (114)434 (155)2157 (1161)1.3e4 (1e4)3/15
CGA-ring16 holtschulte noiseless 1.4 (1)4.5 (4)23 (10)60 (27)139 (89)1018 (560)1.9e4 (1e4)4/15
CMAES Hutter hutter noiseless 3.8 (4)3.6 (1)7.4 (2)12 (4)16 (5)33 (22)98 (69)3/15
DE Pal pal noiseless 1.7 (2)2.8 (4)11 (5)19 (10)29 (12)50 (9)68 (10)15/15
GA-100 holtschulte noiseless 2.2 (2)4.1 (4)35 (19)93 (61)268 (133)3024 (2156)1.3e4 (9419)1/15
HCMA loshchilov noiseless 2.7 (0.6)1 (0)1 (0)1 (0)★41 (0)★41 (0)★41 (0)★415/15
HILL holtschulte noiseless 4.3 (5)3.7 (3)9.2 (6)36 (15)122 (95)785 (565)7793 (2e4)7/15
HMLSL pal noiseless 1.6 (1)1.3 (0.2)1.8 (0.8)1.9 (0.6)2.2 (0.8)2.8 (0.8)3.0 (0.5)15/15
IP-10DDr liao noiseless 1.7 (1)3.6 (3)7.7 (2)12 (3)16 (3)24 (2)33 (2)15/15
IP-500 liao noiseless 1.7 (1)3.6 (2)7.7 (3)12 (3)16 (2)24 (2)33 (3)15/15
IPOP400D auger noiseless 1.4 (1)2.3 (1)6.1 (3)11 (4)15 (7)26 (5)36 (11)15/15
IP liao noiseless 1.7 (1)3.6 (2)7.7 (3)12 (2)16 (2)24 (1)33 (1)15/15
MEMPSODE voglis noiseless 2.8 (2)5.2 (4)15 (7)21 (10)27 (9)47 (15)71 (26)15/15
MLSL pal noiseless 1.6 (1)1.3 (0.6)1.8 (0.8)1.9 (0.6)2.2 (0.2)2.8 (1)3.0 (0.2)15/15
OQNLP pal noiseless 4.0 (3)2.1 (0.7)2.7 (0.6)3.0 (0.8)3.1 (0.6)3.2 (0.6)3.3 (0.7)15/15
P-DCN tran noiseless 0.93 (0.6)8.3 (11)19 (13)25 (10)33 (18)90 (39)196 (82)15/15
P-zero tran noiseless 0.93 (0.8)5.7 (6)13 (9)18 (9)23 (16)64 (32)408 (352)15/15
PRCGA sawyerr noiseless 1.9 (2)5.4 (5)19 (52)36 (40)67 (100)127 (147)192 (163)15/15
SMAC-BBOB hutter noiseless 1.4 (1)1.1 (0.2)2.0 (0.6)2.9 (0.8)5.3 (7)72 (60)2000/15
U-DCN tran noiseless 0.93 (0.8)4.2 (1)15 (9)39 (24)97 (62)292 (207)1630 (970)15/15
U-zero tran noiseless 0.93 (0.4)4.8 (3)15 (6)53 (40)171 (151)1077 (1650)1.8e4 (2e4)15/15
fmincon pal noiseless 1.6 (0.8)1.3 (0.9)1.8 (0.8)1.9 (0.5)2.2 (0.5)2.8 (0.6)3.0 (0.2)15/15
fminunc pal noiseless 1.9 (2)1 (0.5)1.1 (0.1)1.2 (0)1.2 (0)1.2 (0)1.2 (0)15/15
lmm-CMA-ES auger noiseless 1.8 (2)2.0 (1)3.3 (0.4)4.0 (1)5.0 (0.9)6.2 (1)8.2 (0.3)15/15
simplex pal noiseless 12 (15)8.4 (5)11 (5)13 (4)15 (4)17 (2)19 (3)15/15
tany liao noiseless 2.6 (2)2.1 (1)6.7 (2)11 (1)15 (3)23 (2)31 (3)15/15
texp liao noiseless 4.6 (6)3.2 (2)6.0 (2)9.3 (3)13 (7)22 (3)31 (5)15/15

Δ fopt
f2, 2-D
1e1
16
1e0
19
1e-1
25
1e-2
25
1e-3
26
1e-5
28
1e-7
29
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.1 (0.4)3.0 (0.5)2.6 (0.2)2.8 (0.2)2.9 (0.5)3.1 (0.4)3.6 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 7.2 (2)7.3 (2)6.0 (2)6.4 (0.9)6.5 (2)6.8 (2)7.4 (1)15/15
CGA-grid100 holtschulte noiseless 107 (63)286 (113)607 (631)3056 (3357)1.2e4 (1e4)1e50/15
CGA-grid16 holtschulte noiseless 138 (247)321 (195)882 (626)2759 (3075)8639 (8032)5.3e4 (7e4)1e50/15
CGA-ring100 holtschulte noiseless 107 (99)345 (385)963 (1024)2355 (1058)5867 (6855)2.4e4 (3e4)1e50/15
CGA-ring16 holtschulte noiseless 62 (57)272 (342)1016 (1002)4251 (3561)2.6e4 (2e4)1e50/15
CMAES Hutter hutter noiseless 20 (34)38 (20)61 (60)2060/15
DE Pal pal noiseless 10 (1)12 (4)12 (2)14 (3)16 (2)19 (2)22 (3)15/15
GA-100 holtschulte noiseless 88 (87)284 (373)496 (369)3091 (1993)6331 (7917)5.2e4 (6e4)1e50/15
HCMA loshchilov noiseless 2.8 (4)4.5 (4)4.8 (3)5.6 (3)5.7 (3)5.9 (3)6.2 (3)15/15
HILL holtschulte noiseless 80 (127)162 (171)627 (785)5400 (3704)1.7e4 (2e4)1e50/15
HMLSL pal noiseless 1.5 (0.6)1.5 (0.5)1.3 (0.5)1.4 (0.3)1.6 (0.5)2.1 (0.9)2.8 (0.7)15/15
IP-10DDr liao noiseless 17 (13)26 (2)23 (3)25 (2)25 (2)26 (1)27 (2)15/15
IP-500 liao noiseless 17 (14)26 (7)23 (2)25 (3)25 (2)26 (1)27 (1)15/15
IPOP400D auger noiseless 13 (13)19 (9)16 (6)18 (6)19 (3)20 (2)21 (3)15/15
IP liao noiseless 17 (14)26 (2)23 (2)25 (2)25 (1)26 (1)27 (2)15/15
MEMPSODE voglis noiseless 33 (37)64 (52)64 (36)69 (22)67 (20)62 (19)60 (18)15/15
MLSL pal noiseless 1.5 (0.4)1.5 (0.6)1.3 (0.4)1.4 (0.4)1.6 (0.4)2.1 (1)2.8 (0.6)15/15
OQNLP pal noiseless 2.1 (0.2)3.6 (2)3.0 (0.8)3.1 (4)3.2 (4)3.2 (3)17 (8)6/15
P-DCN tran noiseless 8.5 (5)16 (11)28 (15)49 (28)89 (32)278 (265)1592 (296)15/15
P-zero tran noiseless 11 (8)26 (19)30 (13)102 (124)259 (341)2380 (2045)2.7e4 (3e4)7/15
PRCGA sawyerr noiseless 15 (6)18 (10)25 (3)38 (50)53 (157)92 (35)108 (105)15/15
SMAC-BBOB hutter noiseless 3.5 (2)11 (21)36 (34)2000/15
U-DCN tran noiseless 64 (118)173 (50)202 (195)1524 (119)1812 (2106)3444 (6613)2.1e4 (2e4)11/15
U-zero tran noiseless 206 (323)859 (1694)2370 (1291)8581 (8101)1.7e4 (1e4)1.7e5 (1e5)4.9e5 (4e5)0/15
fmincon pal noiseless 1.5 (0.3)1.5 (0.2)1.3 (0.5)1.4 (0.4)1.6 (0.3)2.1 (1)2.8 (0.7)15/15
fminunc pal noiseless 1.9 (2)3.0 (2)3.2 (0.8)3.6 (1)3.7 (2)3.9 (2)4.0 (1)15/15
lmm-CMA-ES auger noiseless 3.1 (2)4.9 (1)4.5 (0.5)4.9 (0.7)4.9 (0.8)4.9 (0.4)5.3 (0.6)15/15
simplex pal noiseless 3.7 (0.8)4.6 (1)4.5 (1)5.2 (0.8)5.2 (0.7)5.4 (0.5)5.7 (0.6)15/15
tany liao noiseless 10 (9)21 (10)20 (2)23 (2)24 (3)25 (2)27 (2)15/15
texp liao noiseless 9.2 (8)20 (13)18 (9)21 (6)23 (2)24 (3)25 (3)15/15

Δ fopt
f3, 2-D
1e1
15
1e0
271
1e-1
445
1e-2
446
1e-3
450
1e-5
454
1e-7
464
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.2 (1)0.81 (2)0.82 (0.6)0.86 (0.1)0.94 (1)1.0 (0.6)1.1 (1)15/15
BIPOP-saACM-k loshchilov noiseless 6.3 (8)2.8 (5)4.7 (4)6.1 (10)6.3 (8)6.3 (8)6.9 (5)15/15
CGA-grid100 holtschulte noiseless 9.5 (8)10 (8)19 (21)51 (9)221 (227)1e50/15
CGA-grid16 holtschulte noiseless 5.9 (5)3.4 (3)5.4 (3)18 (16)53 (65)540 (466)1e50/15
CGA-ring100 holtschulte noiseless 12 (11)6.4 (3)10 (5)19 (14)50 (22)260 (157)1e50/15
CGA-ring16 holtschulte noiseless 6.4 (11)2.4 (1.0)4.7 (6)17 (17)34 (25)310 (307)1e50/15
CMAES Hutter hutter noiseless 4.2 (8)3.5 (6)3.3 (6)6.9 (12)6.8 (7)2060/15
DE Pal pal noiseless 3.6 (2)0.98 (0.4)0.81 (0.2)0.96 (0.3)1.1 (0.4)1.4 (0.3)1.6 (0.4)15/15
GA-100 holtschulte noiseless 5.7 (8)4.9 (2)8.9 (8)26 (19)51 (37)1589 (2214)1e50/15
HCMA loshchilov noiseless 2.2 (2)0.63 (0.1)0.94 (0.2)0.97 (2)1.00 (0.1)1.1 (0.1)1.1 (0.1)15/15
HILL holtschulte noiseless 2.3 (2)1.3 (0.9)2.7 (1)8.5 (4)33 (21)447 (235)1e50/15
HMLSL pal noiseless 5.8 (6)1.1 (0.8)1.7 (0.5)1.9 (1)2.0 (2)2.1 (1)2.1 (1)15/15
IP-10DDr liao noiseless 3.0 (1)2.9 (2)5.0 (7)5.2 (6)5.4 (6)5.5 (5)5.6 (6)15/15
IP-500 liao noiseless 3.0 (1)2.9 (4)4.9 (3)5.0 (4)5.2 (4)5.4 (4)5.6 (5)15/15
IPOP400D auger noiseless 2.4 (2)3.5 (2)9.5 (3)12 (14)12 (14)12 (22)12 (14)4/15
IP liao noiseless 3.0 (2)2.9 (3)4.9 (4)5.0 (6)5.2 (4)5.4 (7)5.6 (6)15/15
MEMPSODE voglis noiseless 5.2 (4)4.7 (8)8.2 (8)8.4 (8)8.4 (8)8.6 (6)8.9 (3)15/15
MLSL pal noiseless 6.1 (5)1.4 (1)4.7 (4)4.7 (5)4.6 (3)4.6 (5)4.5 (6)15/15
OQNLP pal noiseless 12 (7)1.9 (1.0)2.1 (2)2.2 (2)2.2 (2)2.2 (2)2.1 (1)15/15
P-DCN tran noiseless 13 (4)123 (332)283 (435)282 (361)280 (304)279 (147)277 (390)15/15
P-zero tran noiseless 25 (152)180 (338)419 (339)418 (298)415 (259)414 (282)433 (267)15/15
PRCGA sawyerr noiseless 3.1 (3)5.4 (20)7.5 (13)8.0 (12)8.6 (7)9.3 (8)10 (8)15/15
SMAC-BBOB hutter noiseless 3.0 (2)2.5 (2)3.3 (4)2000/15
U-DCN tran noiseless 4.5 (2)3.3 (2)3.1 (2)4.4 (5)7.3 (5)244 (486)1063 (2000)12/15
U-zero tran noiseless 4.5 (3)3.7 (2)7.5 (2)13 (18)73 (64)779 (1079)1.2e4 (1e4)0/15
fmincon pal noiseless 5.7 (5)1.3 (1)6.9 (5)6.9 (7)6.9 (8)6.8 (3)6.7 (8)15/15
fminunc pal noiseless 5.0 (4)2.3 (4)5.5 (7)5.5 (8)5.5 (5)5.4 (3)5.3 (8)15/15
lmm-CMA-ES auger noiseless 2.6 (7)1.8 (2)3.1 (0.7)3.5 (2)4.1 (9)4.2 (7)4.1 (1)9/15
simplex pal noiseless 14 (7)3.0 (1)8.9 (7)8.9 (6)8.8 (6)8.8 (5)8.6 (5)15/15
tany liao noiseless 2.8 (2)3.0 (2)5.2 (4)6.7 (8)7.4 (8)7.6 (8)7.6 (9)15/15
texp liao noiseless 4.0 (5)4.2 (7)5.9 (3)6.2 (5)6.3 (5)6.6 (9)6.7 (7)15/15

Δ fopt
f4, 2-D
1e1
22
1e0
344
1e-1
459
1e-2
496
1e-3
523
1e-5
544
1e-7
566
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.8 (1)1.8 (0.2)11 (0.2)14 (0.5)22 (77)21 (0.4)21 (15)15/15
BIPOP-saACM-k loshchilov noiseless 2.7 (3)7.8 (5)26 (37)38 (48)75 (129)108 (134)105 (125)15/15
CGA-grid100 holtschulte noiseless 14 (17)12 (7)20 (6)43 (29)162 (354)1e50/15
CGA-grid16 holtschulte noiseless 6.0 (4)2.7 (0.9)6.8 (6)23 (20)44 (29)2751 (2665)1e50/15
CGA-ring100 holtschulte noiseless 12 (7)6.9 (3)12 (7)30 (21)62 (37)1344 (1517)1e50/15
CGA-ring16 holtschulte noiseless 5.3 (4)3.2 (2)4.6 (3)14 (13)42 (30)1328 (1511)1e50/15
CMAES Hutter hutter noiseless 2.2 (2)8.8 (14)6.6 (9)2060/15
DE Pal pal noiseless 3.2 (2)0.92 (0.7)7.2 (0.2)6.8 (0.3)6.6 (19)6.6 (0.3)6.6 (35)14/15
GA-100 holtschulte noiseless 6.9 (6)4.6 (2)8.7 (10)24 (18)100 (111)908 (789)1e50/15
HCMA loshchilov noiseless 2.0 (1)1.4 (2)4.5 (11)11 (0.4)11 (0.5)11 (62)11 (30)15/15
HILL holtschulte noiseless 1.7 (1)1.4 (0.6)3.8 (3)12 (3)24 (11)440 (415)1e50/15
HMLSL pal noiseless 4.7 (4)1.2 (1.0)5.5 (14)5.2 (14)5.0 (0.8)4.9 (13)4.7 (11)15/15
IP-10DDr liao noiseless 10 (9)13 (10)91 (114)99 (86)94 (118)91 (109)88 (66)15/15
IP-500 liao noiseless 10 (19)8.3 (6)32 (43)76 (67)77 (60)83 (58)82 (63)15/15
IPOP400D auger noiseless 4.1 (18)6.0 (3)24 (17)22 (17)21 (30)20 (23)20 (38)2/15
IP liao noiseless 10 (15)8.3 (3)33 (44)78 (56)80 (60)100 (89)101 (65)15/15
MEMPSODE voglis noiseless 3.6 (1)2.6 (3)8.6 (8)8.2 (8)8.0 (7)7.9 (7)11 (6)15/15
MLSL pal noiseless 4.9 (5)1.6 (2)13 (11)12 (26)11 (13)11 (19)10 (13)14/15
OQNLP pal noiseless 8.7 (3)6.2 (3)11 (5)10 (14)10 (9)10 (9)9.2 (10)6/15
P-DCN tran noiseless 5.4 (7)208 (335)517 (1040)479 (964)454 (342)438 (878)425 (321)15/15
P-zero tran noiseless 2.5 (1)141 (12)552 (20)511 (18)485 (17)471 (256)516 (63)15/15
PRCGA sawyerr noiseless 2.8 (1)4.0 (5)10 (17)16 (18)20 (25)24 (19)26 (24)15/15
SMAC-BBOB hutter noiseless 2.5 (3)8.4 (8)2000/15
U-DCN tran noiseless 3.7 (2)2.4 (2)3.1 (1)4.6 (2)8.9 (7)64 (33)542 (1902)11/15
U-zero tran noiseless 3.2 (2)3.0 (2)7.6 (4)19 (15)61 (81)693 (888)1.6e4 (1e4)1/15
fmincon pal noiseless 4.6 (4)2.4 (2)9.4 (7)8.8 (7)8.3 (15)8.0 (17)7.7 (6)14/15
fminunc pal noiseless 3.5 (4)2.8 (0.9)10 (13)10 (20)9.2 (6)8.9 (14)8.5 (11)15/15
lmm-CMA-ES auger noiseless 2.2 (1)4.3 (4)51 (75)47 (16)45 (52)43 (35)41 (61)1/15
simplex pal noiseless 11 (4)3.0 (2)13 (13)12 (12)11 (9)11 (10)10 (12)15/15
tany liao noiseless 4.3 (16)7.6 (9)112 (139)138 (129)137 (113)131 (84)127 (100)15/15
texp liao noiseless 1.0 (1)11 (9)113 (132)193 (160)195 (121)192 (147)184 (125)15/15

Δ fopt
f5, 2-D
1e1
4.0
1e0
4.0
1e-1
4.0
1e-2
4.0
1e-3
4.0
1e-5
4.0
1e-7
4.0
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.1 (0.4)1.5 (0)1.5 (0)1.5 (0)1.5 (0)1.5 (0)1.5 (0)15/15
BIPOP-saACM-k loshchilov noiseless 3.2 (1)5.5 (2)5.8 (2)6.1 (2)6.1 (4)6.1 (3)6.1 (2)15/15
CGA-grid100 holtschulte noiseless 5.0 (8)71 (42)93 (54)93 (88)93 (62)93 (41)93 (52)15/15
CGA-grid16 holtschulte noiseless 3.8 (5)31 (6)37 (25)38 (26)38 (26)38 (24)38 (19)15/15
CGA-ring100 holtschulte noiseless 5.6 (3)61 (25)86 (41)86 (45)86 (39)86 (47)86 (36)15/15
CGA-ring16 holtschulte noiseless 5.0 (6)28 (13)36 (17)36 (17)36 (19)36 (19)36 (24)15/15
CMAES Hutter hutter noiseless 3.2 (2)5.7 (5)6.1 (5)6.1 (4)6.1 (2)6.1 (4)6.1 (4)15/15
DE Pal pal noiseless 4.0 (2)32 (13)75 (17)120 (17)170 (24)247 (22)347 (19)15/15
GA-100 holtschulte noiseless 4.7 (5)48 (23)61 (48)65 (35)65 (32)65 (38)65 (21)15/15
HCMA loshchilov noiseless 1.1 (0.2)1.6 (0.1)1.7 (0.2)1.7 (0.1)1.7 (0.2)1.7 (0.2)1.7 (0.2)15/15
HILL holtschulte noiseless 3.2 (2)7.0 (4)7.9 (4)8.0 (8)8.0 (6)8.0 (7)8.0 (6)15/15
HMLSL pal noiseless 1 (0)2.8 (0)3.5 (0)4.2 (0)4.2 (0)5.0 (0)5.8 (0)15/15
IP-10DDr liao noiseless 1.6 (0.1)4.0 (0.5)4.2 (0.5)4.2 (2)4.2 (2)4.2 (2)4.2 (0.5)15/15
IP-500 liao noiseless 1.6 (0.1)4.0 (0.5)4.2 (0.5)4.2 (0.5)4.2 (2)4.2 (2)4.2 (0.5)15/15
IPOP400D auger noiseless 3.2 (1)5.4 (3)6.1 (2)6.1 (3)6.1 (3)6.1 (2)6.1 (2)15/15
IP liao noiseless 1.6 (0.1)4.0 (0.5)4.2 (2)4.2 (3)4.2 (0.5)4.2 (0.5)4.2 (0.5)15/15
MEMPSODE voglis noiseless 2.3 (1)7.1 (5)9.1 (7)9.2 (7)9.2 (4)9.2 (6)9.2 (5)15/15
MLSL pal noiseless 1 (0)2.8 (0)3.5 (0)4.2 (0)4.2 (0)5.0 (0)5.8 (0)15/15
OQNLP pal noiseless 3.8 (0)4.5 (0)4.5 (0)4.5 (0)4.5 (0)4.5 (0)4.5 (0)15/15
P-DCN tran noiseless 2.2 (1)89 (48)123 (53)134 (78)144 (46)180 (40)218 (61)15/15
P-zero tran noiseless 2.8 (2)55 (48)74 (49)82 (56)89 (48)106 (41)120 (40)15/15
PRCGA sawyerr noiseless 104 (26)1039 (928)2211 (1294)3194 (1932)4512 (2661)1.2e4 (1e4)1.9e5 (3e5)1/15
SMAC-BBOB hutter noiseless 0.95 (0.1)1.2 (0.2)1.2 (0.2)1.2 (0.2)1.2 (0.2)1.2 (0.2)1.2 (0.2)15/15
U-DCN tran noiseless 2.2 (1)104 (77)590 (746)1636 (1344)2298 (2794)5.4e5 (7e5)3.6e6 (5e6)1/15
U-zero tran noiseless 1.8 (0.4)52 (28)972 (291)1.4e4 (2057)1.5e5 (7e4)2e60/15
fmincon pal noiseless 1 (0)2.8 (0)3.5 (0)4.2 (0)4.2 (0)5.0 (0)5.8 (0)15/15
fminunc pal noiseless 1.8 (0)3.2 (0)3.2 (0)3.2 (0)3.2 (0)3.2 (0)3.2 (0)15/15
lmm-CMA-ES auger noiseless 3.4 (0.8)5.5 (2)5.7 (3)5.7 (3)5.7 (2)5.7 (2)5.7 (1)15/15
simplex pal noiseless 10 (0.1)40 (44)40 (45)40 (45)40 (45)40 (45)40 (23)15/15
tany liao noiseless 1.9 (0.2)6.3 (5)9.4 (6)9.4 (6)9.4 (1)9.4 (6)9.4 (8)15/15
texp liao noiseless 5.2 (0.8)46 (31)48 (30)48 (30)48 (23)48 (30)48 (21)15/15

Δ fopt
f6, 2-D
1e1
13
1e0
23
1e-1
41
1e-2
54
1e-3
67
1e-5
95
1e-7
124
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.1 (4)4.6 (4)4.2 (2)4.3 (2)4.4 (0.9)4.3 (1)4.3 (0.9)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (3)3.9 (6)4.0 (1)4.5 (5)4.3 (3)4.3 (2)4.7 (4)15/15
CGA-grid100 holtschulte noiseless 3.3 (5)22 (25)78 (94)349 (360)1558 (2091)1e50/15
CGA-grid16 holtschulte noiseless 3.5 (3)17 (20)37 (21)155 (146)827 (1343)3322 (2041)1e50/15
CGA-ring100 holtschulte noiseless 3.0 (4)13 (13)63 (46)137 (73)612 (541)4942 (3357)1e50/15
CGA-ring16 holtschulte noiseless 2.8 (2)13 (7)25 (15)85 (65)222 (393)3367 (4929)1e50/15
CMAES Hutter hutter noiseless 2.4 (4)3.5 (2)4.1 (2)4.5 (3)15 (12)32 (48)2060/15
DE Pal pal noiseless 1.7 (1.0)3.4 (2)5.0 (2)7.2 (2)8.5 (3)9.5 (3)10 (3)15/15
GA-100 holtschulte noiseless 2.4 (2)16 (15)40 (30)132 (102)621 (365)7467 (4611)1e50/15
HCMA loshchilov noiseless 3.0 (2)5.8 (1)4.6 (1)4.7 (3)4.6 (2)4.9 (2)4.8 (2)15/15
HILL holtschulte noiseless 1.6 (2)5.5 (5)11 (10)43 (34)218 (201)2032 (2789)1e50/15
HMLSL pal noiseless 1.6 (0.9)1.6 (0.7)1.3 (0.5)1.1 (0.3)1.1 (0.4)1.1 (0.6)1.4 (0.2)15/15
IP-10DDr liao noiseless 1.4 (1.0)3.7 (2)3.8 (2)3.7 (1)3.8 (1)4.1 (0.8)4.3 (0.8)15/15
IP-500 liao noiseless 1.4 (1)3.7 (3)3.8 (0.7)3.7 (1)3.8 (1)4.1 (0.9)4.3 (1)15/15
IPOP400D auger noiseless 2.4 (1)4.3 (2)3.7 (1)3.8 (1)4.2 (1)4.3 (1)4.2 (0.7)15/15
IP liao noiseless 1.4 (1)3.7 (1)3.8 (1)3.7 (2)3.8 (1)4.1 (1)4.3 (1.0)15/15
MEMPSODE voglis noiseless 3.2 (4)4.1 (2)4.8 (2)5.5 (2)6.0 (2)6.9 (2)10 (13)15/15
MLSL pal noiseless 1.6 (1.0)1.6 (1)1.3 (0.5)1.1 (0.4)1.1 (0.4)1.1 (0.4)1.4 (1)15/15
OQNLP pal noiseless 2.3 (1)2.5 (0.6)1.8 (0.8)1.6 (0.5)1.4 (0.5)2.3 (2)3.6 (4)15/15
P-DCN tran noiseless 3.8 (5)6.6 (2)5.9 (2)6.5 (3)12 (7)32 (37)206 (61)15/15
P-zero tran noiseless 4.3 (3)8.1 (9)6.6 (6)6.6 (4)11 (7)76 (55)2728 (2047)14/15
PRCGA sawyerr noiseless 2.2 (4)26 (35)108 (244)153 (165)157 (276)175 (223)176 (347)15/15
SMAC-BBOB hutter noiseless 1.2 (0.8)9.2 (10)2000/15
U-DCN tran noiseless 1.5 (1)6.2 (6)15 (17)97 (39)160 (112)3077 (7066)4.8e4 (3e4)1/15
U-zero tran noiseless 0.95 (0.6)12 (7)40 (74)152 (155)2582 (556)1.3e4 (2e4)2.3e5 (3e5)0/15
fmincon pal noiseless 1.6 (0.9)1.6 (0.7)1.3 (0.7)1.1 (0.4)1.1 (0.6)1.1 (0.4)1.6 (1)15/15
fminunc pal noiseless 1.8 (2)2.5 (2)1.8 (1)1.9 (0.9)1.8 (0.8)2.0 (2)1.9 (0.6)15/15
lmm-CMA-ES auger noiseless 2.2 (2)2.5 (2)2.5 (0.9)2.6 (0.8)2.7 (0.6)2.7 (0.7)2.7 (0.9)15/15
simplex pal noiseless 4.5 (3)4.3 (1)2.9 (0.9)2.5 (0.7)2.2 (0.6)1.9 (0.6)1.7 (0.1)15/15
tany liao noiseless 1.5 (0.7)2.9 (1)2.9 (0.5)3.1 (0.4)3.2 (0.8)3.9 (0.5)4.1 (0.6)15/15
texp liao noiseless 2.3 (2)3.8 (3)3.6 (3)4.0 (2)4.1 (2)4.4 (1)4.8 (1.0)15/15

Δ fopt
f7, 2-D
1e1
3.0
1e0
21
1e-1
60
1e-2
193
1e-3
217
1e-5
217
1e-7
241
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.6 (3)3.8 (4)2.7 (2)1.2 (0.8)1.2 (0.8)1.2 (0.7)1.4 (0.8)15/15
BIPOP-saACM-k loshchilov noiseless 5.7 (14)4.8 (4)3.0 (3)1.2 (0.8)1.4 (0.7)1.4 (1)1.5 (0.7)15/15
CGA-grid100 holtschulte noiseless 6.8 (2)8.6 (7)19 (18)44 (94)75 (87)75 (94)106 (56)10/15
CGA-grid16 holtschulte noiseless 4.5 (4)4.7 (6)11 (23)18 (7)46 (98)46 (95)64 (133)12/15
CGA-ring100 holtschulte noiseless 4.4 (5)7.5 (12)16 (14)16 (11)33 (63)33 (62)57 (34)15/15
CGA-ring16 holtschulte noiseless 7.4 (9)4.2 (3)10 (19)19 (17)25 (43)25 (19)27 (25)15/15
CMAES Hutter hutter noiseless 6.3 (5)4.4 (4)2.7 (4)1.5 (0.6)1.7 (2)1.7 (1)2.4 (2)3/15
DE Pal pal noiseless 4.9 (3)3.1 (3)3.5 (2)1.5 (0.6)1.7 (0.6)1.7 (0.4)2.0 (0.7)15/15
GA-100 holtschulte noiseless 2.6 (3)4.3 (7)12 (4)15 (13)23 (16)23 (23)39 (27)15/15
HCMA loshchilov noiseless 3.0 (1)3.9 (3)2.7 (2)1.6 (1)1.7 (0.6)1.7 (1.0)1.7 (0.8)15/15
HILL holtschulte noiseless 6.6 (7)7.0 (12)10 (10)44 (104)71 (114)71 (137)70 (49)15/15
HMLSL pal noiseless 4.2 (4)3.5 (4)4.5 (2)2.8 (2)3.2 (1)3.2 (0.9)3.4 (1)15/15
IP-10DDr liao noiseless 4.3 (4)7.2 (11)4.1 (5)1.7 (0.9)1.7 (2)1.7 (1)1.8 (1)15/15
IP-500 liao noiseless 4.3 (3)7.2 (13)4.1 (4)1.7 (1)1.7 (2)1.7 (1)1.8 (1)15/15
IPOP400D auger noiseless 3.4 (2)3.5 (3)3.5 (3)1.6 (1)1.5 (1.0)1.5 (1)1.6 (1.0)15/15
IP liao noiseless 4.3 (5)7.2 (10)4.1 (4)1.7 (2)1.7 (2)1.7 (2)1.8 (2)15/15
MEMPSODE voglis noiseless 5.9 (4)16 (20)25 (23)10 (8)11 (7)11 (9)11 (6)15/15
MLSL pal noiseless 5.1 (5)6.6 (11)18 (25)56 (49)135 (276)135 (232)122 (188)7/15
OQNLP pal noiseless 6.9 (8)2.7 (3)3.4 (1)1.6 (0.5)1.8 (0.9)1.8 (0.9)2.1 (0.6)13/15
P-DCN tran noiseless 24 (46)1.5e4 (81)5153 (35)1603 (5182)1426 (9)1426 (6914)1284 (7)13/15
P-zero tran noiseless 11 (21)1.5e4 (7e4)5289 (8377)1645 (20)1463 (2414)1463 (4613)1318 (2086)13/15
PRCGA sawyerr noiseless 3.8 (14)5.6 (15)7.0 (4)3.9 (4)4.6 (7)4.6 (8)5.0 (3)15/15
SMAC-BBOB hutter noiseless 2.1 (2)1.1 (1)1.1 (0.5)2.5 (1)14 (19)14 (20)2000/15
U-DCN tran noiseless 6.0 (8)4.0 (5)41 (29)111 (210)272 (379)272 (362)248 (367)15/15
U-zero tran noiseless 5.4 (6)3.9 (6)70 (198)122 (59)193 (330)193 (133)183 (315)15/15
fmincon pal noiseless 4.1 (4)5.9 (5)16 (18)58 (48)196 (224)196 (246)177 (132)6/15
fminunc pal noiseless 5.3 (8)3.9 (4)28 (23)80 (67)125 (111)125 (96)136 (75)7/15
lmm-CMA-ES auger noiseless 3.7 (2)2.2 (3)1.3 (0.6)0.58 (1.0)0.60 (0.5)0.60 (0.3)0.60 (0.3)15/15
simplex pal noiseless 5.8 (10)4.1 (2)6.8 (12)7.8 (9)11 (10)11 (14)10 (7)15/15
tany liao noiseless 3.9 (3)6.0 (9)5.7 (7)2.1 (2)2.0 (1)2.0 (2)2.0 (2)15/15
texp liao noiseless 4.1 (4)4.0 (8)4.2 (3)1.6 (0.5)1.5 (0.8)1.5 (0.8)1.7 (0.7)15/15

Δ fopt
f8, 2-D
1e1
5.0
1e0
12
1e-1
37
1e-2
46
1e-3
86
1e-5
94
1e-7
112
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 6.6 (7)13 (17)9.1 (7)9.1 (6)5.3 (4)5.7 (2)5.3 (2)15/15
BIPOP-saACM-k loshchilov noiseless 4.6 (2)9.4 (8)5.5 (5)5.7 (4)3.3 (2)3.4 (2)3.0 (1)15/15
CGA-grid100 holtschulte noiseless 6.2 (3)27 (21)57 (127)510 (665)1218 (847)1e50/15
CGA-grid16 holtschulte noiseless 11 (13)33 (20)67 (98)452 (408)1163 (501)1e50/15
CGA-ring100 holtschulte noiseless 8.9 (27)27 (17)50 (38)176 (231)383 (402)2758 (3274)1e50/15
CGA-ring16 holtschulte noiseless 9.1 (10)17 (18)45 (64)197 (298)568 (342)1.5e4 (2e4)1e50/15
CMAES Hutter hutter noiseless 10 (4)9.1 (9)11 (13)15 (25)12 (26)2060/15
DE Pal pal noiseless 7.3 (7)12 (13)10 (5)12 (8)9.0 (2)11 (2)12 (2)15/15
GA-100 holtschulte noiseless 8.1 (9)17 (19)30 (24)102 (68)326 (259)7563 (9504)1e50/15
HCMA loshchilov noiseless 2.1 (0.8)7.2 (11)7.1 (4)7.6 (2)4.4 (1)4.4 (1)3.8 (0.9)15/15
HILL holtschulte noiseless 10 (8)43 (24)43 (71)456 (557)1368 (1259)1e50/15
HMLSL pal noiseless 2.6 (3)4.0 (3)1.9 (1)1.8 (1)1.0 (0.6)1.1 (0.5)0.95 (0.5)15/15
IP-10DDr liao noiseless 3.3 (3)6.2 (3)9.0 (3)9.4 (1)5.9 (2)6.3 (2)6.0 (1)15/15
IP-500 liao noiseless 3.3 (2)6.2 (1)9.0 (4)9.4 (5)5.9 (2)6.3 (1)6.0 (0.4)15/15
IPOP400D auger noiseless 3.7 (3)10 (16)8.3 (6)10 (5)5.9 (3)6.3 (2)5.8 (2)15/15
IP liao noiseless 3.3 (2)6.2 (11)9.0 (7)9.4 (3)5.9 (3)6.3 (2)6.0 (1)15/15
MEMPSODE voglis noiseless 13 (5)25 (3)22 (27)30 (18)19 (9)18 (7)16 (5)15/15
MLSL pal noiseless 2.6 (1)4.0 (2)1.9 (2)1.8 (1)1.0 (0.8)1.1 (0.6)0.95 (0.5)15/15
OQNLP pal noiseless 2.7 (2)2.9 (4)1.8 (1)1.8 (1)1.1 (0.3)1.1 (0.6)1.5 (0.5)14/15
P-DCN tran noiseless 14 (12)41 (11)46 (88)60 (55)46 (52)114 (55)1553 (1314)15/15
P-zero tran noiseless 51 (169)114 (39)58 (89)65 (91)46 (32)262 (262)3.7e4 (7e4)3/15
PRCGA sawyerr noiseless 5.1 (5)5.0 (4)50 (94)112 (230)99 (155)162 (151)193 (97)15/15
SMAC-BBOB hutter noiseless 2.7 (3)5.0 (6)24 (20)2000/15
U-DCN tran noiseless 10 (8)11 (15)37 (20)274 (222)2187 (4041)1.4e5 (2e5)2e60/15
U-zero tran noiseless 5.9 (4)16 (25)146 (255)1480 (1787)5645 (1e4)6.8e4 (2e5)2e60/15
fmincon pal noiseless 2.6 (4)4.0 (3)1.9 (1)1.8 (1)1.0 (0.6)1.1 (0.7)0.95 (0.6)15/15
fminunc pal noiseless 1.9 (2)2.2 (3)1.5 (1)1.6 (0.4)0.95 (0.4)0.94 (0.4)0.83 (0.4)15/15
lmm-CMA-ES auger noiseless 2.7 (2)3.8 (3)2.5 (1)2.7 (1.0)1.6 (0.8)1.7 (0.7)1.5 (0.4)15/15
simplex pal noiseless 6.8 (3)5.2 (3)2.9 (1)2.8 (1)1.6 (0.5)1.7 (0.5)1.5 (0.3)15/15
tany liao noiseless 5.3 (4)6.0 (4)7.9 (4)8.8 (5)5.7 (0.8)5.9 (2)5.8 (1)15/15
texp liao noiseless 5.9 (2)3.5 (2)6.6 (2)8.9 (0.9)5.5 (1)6.0 (0.9)5.7 (1)15/15

Δ fopt
f9, 2-D
1e1
1
1e0
18
1e-1
30
1e-2
44
1e-3
68
1e-5
81
1e-7
92
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 17 (12)7.2 (9)10 (9)9.0 (5)6.7 (3)6.5 (3)6.5 (2)15/15
BIPOP-saACM-k loshchilov noiseless 25 (46)5.3 (3)7.2 (7)6.8 (4)4.7 (2)4.2 (2)3.9 (1)15/15
CGA-grid100 holtschulte noiseless 59 (50)23 (25)86 (38)564 (949)2730 (2159)1e50/15
CGA-grid16 holtschulte noiseless 53 (58)15 (5)37 (20)441 (509)3595 (2443)1e50/15
CGA-ring100 holtschulte noiseless 30 (22)24 (10)60 (61)133 (144)403 (560)8402 (1e4)1e50/15
CGA-ring16 holtschulte noiseless 40 (27)10 (12)32 (82)246 (162)1163 (1623)1e50/15
CMAES Hutter hutter noiseless 24 (20)7.5 (2)9.5 (14)16 (7)22 (17)2060/15
DE Pal pal noiseless 37 (54)7.1 (5)9.1 (4)12 (5)10 (6)12 (5)13 (3)15/15
GA-100 holtschulte noiseless 34 (39)9.4 (10)22 (17)111 (110)542 (729)5475 (2995)1e50/15
HCMA loshchilov noiseless 18 (20)4.4 (7)6.7 (4)5.7 (2)4.2 (2)3.9 (2)3.6 (2)15/15
HILL holtschulte noiseless 36 (25)14 (7)70 (80)378 (458)1245 (2101)5657 (5504)1e50/15
HMLSL pal noiseless 1 (0)0.61 (0)0.77 (0)0.75 (0)0.60 (0.0)0.61 (0.0)0.61 (0.0)15/15
IP-10DDr liao noiseless 30 (20)6.1 (1)10 (10)10 (9)7.4 (3)7.1 (6)7.1 (2)15/15
IP-500 liao noiseless 30 (17)6.1 (3)10 (11)10 (3)7.4 (7)7.1 (3)7.1 (3)15/15
IPOP400D auger noiseless 1 (0)1.6 (1)6.5 (4)6.8 (1)5.2 (0.8)5.4 (1.0)5.5 (0.9)15/15
IP liao noiseless 30 (22)6.1 (2)10 (3)10 (5)7.4 (5)7.1 (3)7.1 (4)15/15
MEMPSODE voglis noiseless 54 (161)19 (22)20 (34)26 (19)22 (9)21 (4)19 (7)15/15
MLSL pal noiseless 1 (0)0.61 (0)0.77 (0)0.75 (0)0.60 (0.0)0.61 (0.0)0.61 (0.0)15/15
OQNLP pal noiseless 1 (0)0.53 (0.0)0.99 (0.0)0.88 (0.1)0.78 (0.1)0.78 (0.0)0.75 (0.0)15/15
P-DCN tran noiseless 31 (9)36 (88)79 (113)78 (74)60 (64)189 (128)1688 (3626)10/15
P-zero tran noiseless 21 (16)63 (113)84 (70)87 (34)72 (53)584 (263)1.2e4 (5151)5/15
PRCGA sawyerr noiseless 30 (15)4.3 (3)62 (154)114 (132)104 (119)143 (138)170 (96)15/15
SMAC-BBOB hutter noiseless 1 (0)4.2 (4)23 (16)2000/15
U-DCN tran noiseless 18 (16)5.6 (3)47 (34)663 (1095)3187 (2201)3.2e4 (4e4)3.1e5 (3e5)1/15
U-zero tran noiseless 22 (30)16 (2)145 (172)1945 (1997)7568 (1e4)4.4e4 (6e4)2e60/15
fmincon pal noiseless 1 (0)0.61 (0)0.77 (0)0.75 (0)0.60 (0.0)0.61 (0.0)0.61 (0.0)15/15
fminunc pal noiseless 1 (0)0.39 (0)0.93 (0)0.95 (0.0)0.74 (0.1)0.73 (0.0)0.68 (0.0)15/15
lmm-CMA-ES auger noiseless 1 (0)2.2 (1)2.8 (2)2.7 (2)2.0 (0.7)1.9 (0.3)1.8 (0.7)15/15
simplex pal noiseless 1 (0)1.4 (0.0)2.3 (0.9)2.1 (0.3)1.6 (0.2)1.5 (0.2)1.5 (0.2)15/15
tany liao noiseless 20 (18)5.2 (4)7.9 (7)9.2 (2)6.7 (1)6.7 (3)6.9 (3)15/15
texp liao noiseless 14 (4)2.2 (2)8.0 (6)8.4 (6)6.3 (3)6.4 (2)6.3 (2)15/15

Δ fopt
f10, 2-D
1e1
30
1e0
46
1e-1
54
1e-2
61
1e-3
68
1e-5
82
1e-7
98
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 7.9 (6)7.5 (3)7.2 (1)7.1 (2)6.7 (0.7)6.2 (0.8)5.8 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 3.8 (2)3.0 (0.5)2.7 (0.5)2.5 (0.2)2.5 (0.5)2.3 (0.5)2.2 (0.2)15/15
CGA-grid100 holtschulte noiseless 309 (517)2491 (3852)2.6e4 (3e4)1e50/15
CGA-grid16 holtschulte noiseless 45 (29)759 (1088)5871 (4874)2.4e4 (2e4)1e50/15
CGA-ring100 holtschulte noiseless 58 (38)208 (326)1697 (1367)4101 (4918)1e50/15
CGA-ring16 holtschulte noiseless 62 (44)268 (267)2856 (3012)7559 (9022)1e50/15
CMAES Hutter hutter noiseless 10 (4)12 (20)28 (33)2060/15
DE Pal pal noiseless 11 (4)11 (3)11 (2)12 (4)12 (2)14 (2)14 (2)15/15
GA-100 holtschulte noiseless 384 (720)1406 (1848)2900 (3312)2.4e4 (5e4)1e50/15
HCMA loshchilov noiseless 3.5 (2)3.7 (0.8)3.4 (0.7)3.2 (0.6)3.1 (0.6)2.9 (0.5)2.7 (0.5)15/15
HILL holtschulte noiseless 264 (268)687 (1902)4669 (3196)2.4e4 (1e4)1e50/15
HMLSL pal noiseless 0.70 (0.1)0.52 (0.1)0.50 (0.1)0.51 (0.1)1.2 (2)11 (32)27 (16)15/15
IP-10DDr liao noiseless 12 (8)11 (4)10 (1)10 (4)10 (1)8.7 (0.9)8.1 (0.8)15/15
IP-500 liao noiseless 12 (8)11 (1)10 (3)10 (3)10 (1)8.7 (1)8.1 (0.8)15/15
IPOP400D auger noiseless 6.0 (5)6.8 (2)7.8 (2)7.9 (1)7.4 (1)6.8 (1)6.3 (0.7)15/15
IP liao noiseless 12 (8)11 (1)10 (3)10 (2)10 (1)8.7 (1)8.1 (0.7)15/15
MEMPSODE voglis noiseless 22 (28)31 (23)29 (15)26 (13)25 (13)25 (13)29 (23)15/15
MLSL pal noiseless 0.70 (0.3)0.52 (0.2)0.50 (0.1)0.51 (0.2)0.99 (1)5.5 (19)91 (92)8/15
OQNLP pal noiseless 1.2 (0.5)1.5 (2)1.3 (0.7)2.4 (3)7.9 (10)17 (36)54 (43)5/15
P-DCN tran noiseless 390 (559)675 (822)840 (376)897 (553)1361 (1043)1.7e4 (3e4)1.3e5 (2e5)1/15
P-zero tran noiseless 382 (420)955 (952)1282 (1249)1347 (498)1530 (568)2.7e4 (3e4)3.1e5 (4e5)1/15
PRCGA sawyerr noiseless 88 (221)658 (673)869 (1024)1351 (1375)1662 (1965)3181 (2134)5856 (6964)2/15
SMAC-BBOB hutter noiseless 1.3 (1)3.0 (4)53 (54)2000/15
U-DCN tran noiseless 162 (318)1287 (1385)5746 (9029)4.7e4 (4e4)2.1e5 (3e5)2e60/15
U-zero tran noiseless 267 (426)994 (1078)9883 (2e4)3.4e4 (7e4)1.2e5 (1e5)2e60/15
fmincon pal noiseless 0.70 (0.2)0.52 (0.1)0.50 (0.1)0.51 (0.2)1.0 (0.9)12 (29)120 (160)9/15
fminunc pal noiseless 1.1 (0.6)1.2 (0.8)1.3 (0.4)1.5 (0.6)1.5 (0.4)6.9 (3)153 (119)7/15
lmm-CMA-ES auger noiseless 2.4 (1)1.9 (0.2)1.9 (0.5)1.9 (0.2)1.8 (0.2)1.7 (0.3)1.5 (0.2)15/15
simplex pal noiseless 2.4 (1)2.3 (0.7)2.2 (0.8)2.1 (0.4)2.0 (0.3)1.9 (0.4)1.7 (0.2)15/15
tany liao noiseless 8.9 (8)8.8 (4)10 (0.7)10 (0.3)9.3 (0.9)8.7 (0.3)7.9 (0.4)15/15
texp liao noiseless 9.4 (6)11 (1)10 (0.7)9.1 (1)8.7 (0.6)8.0 (0.7)7.6 (0.6)15/15

Δ fopt
f11, 2-D
1e1
35
1e0
45
1e-1
50
1e-2
62
1e-3
67
1e-5
81
1e-7
97
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 6.5 (4)7.6 (2)7.7 (0.7)6.7 (0.5)6.7 (1)6.1 (0.7)5.8 (0.9)15/15
BIPOP-saACM-k loshchilov noiseless 2.8 (0.7)2.8 (1.0)3.0 (0.5)2.6 (0.6)2.6 (0.4)2.4 (0.7)2.2 (0.6)15/15
CGA-grid100 holtschulte noiseless 87 (172)1227 (1603)6112 (1e4)1.1e4 (9941)1e50/15
CGA-grid16 holtschulte noiseless 97 (87)807 (881)5405 (4198)2.4e4 (3e4)1e50/15
CGA-ring100 holtschulte noiseless 37 (30)197 (221)1177 (1194)5381 (3180)2.2e4 (2e4)1e50/15
CGA-ring16 holtschulte noiseless 48 (46)557 (579)4830 (8396)7066 (5018)1.0e4 (1e4)1e50/15
CMAES Hutter hutter noiseless 5.2 (5)22 (13)20 (12)2060/15
DE Pal pal noiseless 8.9 (4)10 (2)10 (3)10 (2)12 (2)14 (2)14 (1)15/15
GA-100 holtschulte noiseless 28 (39)2325 (1176)8934 (1e4)2.4e4 (2e4)1e50/15
HCMA loshchilov noiseless 2.6 (2)3.6 (1)3.7 (0.5)3.2 (0.7)3.1 (0.6)2.9 (0.7)2.6 (0.2)15/15
HILL holtschulte noiseless 125 (239)478 (629)2260 (2352)1.2e4 (2e4)1e50/15
HMLSL pal noiseless 0.63 (0.4)0.57 (0.3)0.59 (0.4)0.54 (0.2)0.61 (0.3)11 (23)16 (26)15/15
IP-10DDr liao noiseless 8.1 (6)12 (3)12 (0.7)10 (0.5)10 (0.7)9.2 (0.8)8.3 (0.6)15/15
IP-500 liao noiseless 8.1 (6)12 (1)12 (0.7)10 (0.6)10 (1)9.2 (0.3)8.3 (0.6)15/15
IPOP400D auger noiseless 5.3 (4)8.2 (3)9.1 (1)8.0 (1.0)7.8 (1)7.3 (0.9)6.7 (0.8)15/15
IP liao noiseless 8.1 (7)12 (2)12 (0.5)10 (0.5)10 (0.7)9.2 (0.6)8.3 (0.4)15/15
MEMPSODE voglis noiseless 21 (30)38 (18)37 (19)30 (15)28 (13)29 (8)31 (16)15/15
MLSL pal noiseless 0.63 (0.2)0.57 (0.1)0.59 (0.3)0.54 (0.3)0.61 (0.2)8.8 (4)64 (101)9/15
OQNLP pal noiseless 1.3 (0.2)1.7 (2)2.8 (4)5.6 (6)10 (12)18 (15)51 (50)5/15
P-DCN tran noiseless 159 (354)410 (566)577 (412)568 (393)1149 (952)1.3e4 (2e4)8.8e4 (2e5)2/15
P-zero tran noiseless 174 (562)680 (616)1102 (797)1164 (638)1698 (958)1.5e4 (3e4)1.5e5 (1e5)0/15
PRCGA sawyerr noiseless 42 (44)330 (110)678 (740)1309 (2609)2422 (1963)4226 (3570)6044 (7013)2/15
SMAC-BBOB hutter noiseless 1.4 (1)4.7 (3)60 (59)2000/15
U-DCN tran noiseless 21 (30)709 (1024)9666 (6081)4.4e4 (2e4)2.0e5 (2e5)2e60/15
U-zero tran noiseless 104 (134)675 (1576)1.1e4 (2e4)4.1e4 (5e4)4.2e5 (4e5)2e60/15
fmincon pal noiseless 0.63 (0.2)0.57 (0.3)0.59 (0.4)0.54 (0.3)0.61 (0.2)3.9 (4)73 (54)12/15
fminunc pal noiseless 0.80 (0.5)1.4 (0.6)1.6 (0.3)1.4 (0.5)1.7 (1)3.8 (3)61 (30)12/15
lmm-CMA-ES auger noiseless 2.0 (1)2.0 (1)2.2 (0.5)1.9 (0.4)1.8 (0.2)1.7 (0.2)1.6 (0.3)15/15
simplex pal noiseless 1.9 (0.2)2.5 (0.9)2.5 (0.1)2.1 (0.2)2.1 (0.2)1.9 (0.1)1.7 (0.1)15/15
tany liao noiseless 5.6 (4)10 (4)12 (1)10 (0.5)10 (1)8.9 (0.4)8.3 (0.7)15/15
texp liao noiseless 8.0 (6)11 (3)12 (3)10 (3)10 (3)9.0 (0.8)8.2 (2)15/15

Δ fopt
f12, 2-D
1e1
35
1e0
46
1e-1
75
1e-2
94
1e-3
105
1e-5
153
1e-7
195
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.3 (4)8.7 (2)6.4 (1.0)5.6 (4)5.5 (7)4.5 (3)4.0 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 4.7 (5)5.3 (2)3.8 (4)4.3 (2)4.5 (6)4.0 (4)4.9 (6)15/15
CGA-grid100 holtschulte noiseless 89 (109)793 (631)1314 (2418)2652 (3526)4534 (7381)1e50/15
CGA-grid16 holtschulte noiseless 109 (204)529 (573)1196 (1446)7196 (1e4)1.4e4 (1e4)1e50/15
CGA-ring100 holtschulte noiseless 51 (60)178 (223)513 (291)1474 (1416)6702 (5511)1e50/15
CGA-ring16 holtschulte noiseless 38 (57)218 (479)1393 (1073)4403 (7979)1.3e4 (8571)1e50/15
CMAES Hutter hutter noiseless 13 (13)21 (9)20 (37)32 (22)2060/15
DE Pal pal noiseless 7.5 (21)15 (28)14 (3)16 (45)16 (26)16 (10)16 (19)15/15
GA-100 holtschulte noiseless 30 (24)380 (109)865 (1021)1488 (1322)2139 (3736)1e50/15
HCMA loshchilov noiseless 3.4 (3)5.7 (4)5.8 (1)5.1 (2)5.1 (7)4.6 (5)4.3 (2)15/15
HILL holtschulte noiseless 80 (91)410 (931)1695 (2709)2679 (3758)6766 (6905)1e50/15
HMLSL pal noiseless 0.84 (0.2)1.0 (2)1.00 (2)0.96 (2)0.98 (2)2.8 (0.5)16 (13)15/15
IP-10DDr liao noiseless 9.2 (7)14 (4)14 (11)14 (12)13 (20)11 (15)10 (14)15/15
IP-500 liao noiseless 9.2 (5)14 (19)14 (4)14 (6)13 (16)11 (15)10 (14)15/15
IPOP400D auger noiseless 6.2 (4)9.4 (4)8.0 (5)6.8 (7)7.2 (0.9)5.5 (8)4.7 (3)13/15
IP liao noiseless 9.2 (9)14 (19)14 (23)14 (17)13 (11)11 (12)10 (14)15/15
MEMPSODE voglis noiseless 21 (30)30 (23)21 (4)17 (11)16 (7)13 (3)13 (10)15/15
MLSL pal noiseless 0.84 (2)1.0 (0.7)1.00 (1)0.96 (1)0.98 (0.3)2.4 (2)17 (69)12/15
OQNLP pal noiseless 1.6 (3)2.5 (3)3.0 (3)3.9 (3)8.1 (12)22 (102)47 (47)4/15
P-DCN tran noiseless 73 (84)209 (210)207 (255)317 (263)479 (665)6372 (4223)2.9e4 (3e4)3/15
P-zero tran noiseless 62 (201)296 (320)434 (285)528 (425)714 (568)6518 (1e4)7.0e4 (1e5)0/15
PRCGA sawyerr noiseless 32 (24)275 (652)514 (459)727 (429)685 (775)496 (501)519 (450)8/15
SMAC-BBOB hutter noiseless 3.3 (3)6.8 (6)40 (31)2000/15
U-DCN tran noiseless 41 (111)439 (827)1067 (496)1.2e4 (1e4)1.9e4 (4e4)8.5e4 (6e4)1.4e5 (1e5)1/15
U-zero tran noiseless 73 (140)966 (1424)6644 (4759)1.0e4 (1e4)2.3e4 (5e4)1.9e5 (2e5)2e60/15
fmincon pal noiseless 0.84 (2)1.0 (0.7)1.00 (0.6)0.96 (2)0.98 (0.7)1.4 (2)12 (34)12/15
fminunc pal noiseless 1.1 (0.6)1.7 (0.7)1.7 (1)1.7 (2)1.6 (2)1.9 (2)41 (42)12/15
lmm-CMA-ES auger noiseless 1.9 (1)3.6 (5)3.5 (5)3.4 (2)3.4 (3)3.2 (4)2.9 (2)14/15
simplex pal noiseless 2.4 (2)3.0 (2)2.3 (2)2.1 (0.3)2.0 (2)1.6 (1)1.4 (0.3)15/15
tany liao noiseless 9.4 (7)10 (11)8.2 (3)8.3 (0.9)8.0 (7)6.8 (6)6.1 (4)15/15
texp liao noiseless 6.9 (8)10 (5)9.4 (11)10 (6)10 (11)8.0 (7)7.4 (3)15/15

Δ fopt
f13, 2-D
1e1
23
1e0
35
1e-1
46
1e-2
60
1e-3
71
1e-5
95
1e-7
122
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.8 (0.9)5.9 (3)5.8 (1)5.6 (1)5.5 (0.6)6.0 (0.9)5.7 (0.9)15/15
BIPOP-saACM-k loshchilov noiseless 3.2 (2)3.2 (1)3.2 (2)2.9 (1)2.8 (0.8)2.7 (0.6)2.7 (1)15/15
CGA-grid100 holtschulte noiseless 23 (35)157 (186)3656 (3784)2.4e4 (2e4)1e50/15
CGA-grid16 holtschulte noiseless 14 (25)158 (169)1186 (1702)1.1e4 (5833)1e50/15
CGA-ring100 holtschulte noiseless 15 (13)93 (105)411 (376)2871 (2330)1e50/15
CGA-ring16 holtschulte noiseless 10 (7)177 (70)1499 (2373)5442 (4102)1e50/15
CMAES Hutter hutter noiseless 3.1 (2)5.5 (1)8.8 (5)51 (52)2060/15
DE Pal pal noiseless 4.8 (2)8.0 (3)10 (4)11 (2)13 (4)14 (4)15 (2)15/15
GA-100 holtschulte noiseless 10 (11)86 (77)831 (1724)2754 (2012)2.1e4 (2e4)1e50/15
HCMA loshchilov noiseless 2.9 (3)3.7 (1)3.6 (0.9)3.2 (0.9)3.3 (0.7)3.2 (1)3.0 (1)15/15
HILL holtschulte noiseless 13 (11)150 (192)1986 (1111)1.2e4 (1e4)1e50/15
HMLSL pal noiseless 0.76 (0.4)0.72 (0.2)0.74 (0.1)0.73 (0.2)0.76 (0.1)29 (25)43 (4)15/15
IP-10DDr liao noiseless 4.3 (2)7.6 (6)10 (5)8.5 (4)9.3 (1)8.5 (0.7)9.1 (2)15/15
IP-500 liao noiseless 4.3 (4)7.6 (6)10 (5)8.5 (4)9.3 (1.0)8.5 (0.6)9.1 (1)15/15
IPOP400D auger noiseless 3.6 (4)6.8 (4)7.0 (4)6.9 (2)6.8 (2)7.4 (2)7.1 (1)15/15
IP liao noiseless 4.3 (7)7.6 (6)10 (5)8.5 (4)9.3 (1)8.5 (0.5)9.1 (1)15/15
MEMPSODE voglis noiseless 12 (4)26 (29)25 (21)21 (10)19 (9)15 (4)102 (313)15/15
MLSL pal noiseless 0.76 (0.4)0.72 (0.3)0.74 (0.3)0.73 (0.2)0.76 (0.2)380 (484)2e40/15
OQNLP pal noiseless 1.2 (0.6)1.1 (0.4)0.95 (0.2)1.3 (0.2)2.3 (1)10 (7)386 (280)0/15
P-DCN tran noiseless 20 (5)81 (54)159 (187)285 (230)950 (945)5.9e4 (7e4)2e60/15
P-zero tran noiseless 37 (58)145 (248)221 (277)544 (567)2865 (3233)2e60/15
PRCGA sawyerr noiseless 33 (103)149 (174)726 (771)827 (994)2076 (3849)1.7e4 (1e4)1e50/15
SMAC-BBOB hutter noiseless 1.5 (1.0)6.3 (6)2000/15
U-DCN tran noiseless 10 (15)322 (488)8278 (9932)4.4e4 (5e4)8.8e4 (5e4)2e60/15
U-zero tran noiseless 10 (22)456 (669)7861 (9728)2.0e4 (1e4)2.0e5 (2e5)2e60/15
fmincon pal noiseless 0.76 (0.4)0.72 (0.3)0.74 (0.1)0.73 (0.2)0.76 (0.1)181 (316)2e40/15
fminunc pal noiseless 5.1 (4)12 (14)128 (177)382 (430)724 (602)2e40/15
lmm-CMA-ES auger noiseless 2.0 (0.4)3.1 (1)3.2 (2)2.9 (1)2.8 (0.7)2.9 (0.6)2.8 (0.4)15/15
simplex pal noiseless 4.0 (2)3.9 (2)3.5 (1.0)3.0 (0.7)2.7 (0.7)2.2 (0.4)2.0 (0.4)15/15
tany liao noiseless 5.8 (8)11 (2)10 (2)9.3 (2)8.9 (1)8.3 (0.6)9.1 (0.8)15/15
texp liao noiseless 7.3 (9)9.0 (6)9.2 (4)8.4 (3)8.9 (1)8.2 (2)7.9 (0.8)15/15

Δ fopt
f14, 2-D
1e1
1
1e0
7.0
1e-1
16
1e-2
24
1e-3
38
1e-5
67
1e-7
90
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.3 (2)5.1 (4)5.1 (2)5.6 (3)6.0 (2)5.7 (0.9)6.3 (1)15/15
BIPOP-saACM-k loshchilov noiseless 3.7 (4)3.6 (4)3.8 (2)3.8 (1)3.2 (0.6)2.9 (0.2)2.9 (0.3)15/15
CGA-grid100 holtschulte noiseless 1.7 (2)3.4 (4)34 (21)73 (82)1022 (751)1e50/15
CGA-grid16 holtschulte noiseless 1.8 (2)4.8 (9)14 (12)40 (29)1092 (1365)1e50/15
CGA-ring100 holtschulte noiseless 2.0 (1)4.4 (7)34 (21)88 (72)293 (264)1e50/15
CGA-ring16 holtschulte noiseless 2.9 (2)3.4 (6)12 (6)27 (16)942 (1143)2.2e4 (3e4)1e50/15
CMAES Hutter hutter noiseless 1.9 (0.8)2.7 (3)3.6 (0.9)4.6 (2)12 (9)46 (32)2060/15
DE Pal pal noiseless 2.4 (2)3.9 (4)7.0 (2)7.8 (4)8.4 (2)10 (3)13 (3)15/15
GA-100 holtschulte noiseless 2.9 (3)2.4 (4)30 (24)57 (19)161 (158)2.2e4 (1e4)1e50/15
HCMA loshchilov noiseless 3.2 (3)3.2 (1)3.1 (3)5.0 (3)4.2 (2)3.6 (0.8)3.3 (1)15/15
HILL holtschulte noiseless 5.3 (6)2.7 (1)3.9 (5)47 (43)695 (1379)1e50/15
HMLSL pal noiseless 2.7 (2)1.1 (0.6)1.0 (0.5)1.0 (0.3)0.93 (0.3)1.1 (0.3)21 (19)15/15
IP-10DDr liao noiseless 1.6 (1)2.0 (2)3.6 (0.6)4.3 (0.9)5.0 (3)7.4 (0.6)8.1 (0.6)15/15
IP-500 liao noiseless 1.6 (0.8)2.0 (2)3.6 (1)4.3 (0.8)5.0 (3)7.4 (0.8)8.1 (0.3)15/15
IPOP400D auger noiseless 1.1 (0)2.2 (2)3.0 (1)3.8 (2)4.0 (2)5.8 (2)6.9 (0.8)15/15
IP liao noiseless 1.6 (2)2.0 (2)3.6 (2)4.3 (0.5)5.0 (3)7.4 (0.6)8.1 (0.6)15/15
MEMPSODE voglis noiseless 3.3 (4)3.7 (2)5.5 (2)6.8 (3)11 (12)11 (6)17 (14)15/15
MLSL pal noiseless 2.7 (3)1.1 (0.8)1.0 (0.5)1.0 (0.4)0.93 (0.3)1.1 (0.2)382 (449)4/15
OQNLP pal noiseless 4.8 (6)2.2 (2)1.6 (0.8)1.4 (0.6)1.2 (0.4)2.0 (3)11 (11)5/15
P-DCN tran noiseless 2.0 (1)6.5 (10)7.8 (10)10 (2)12 (11)745 (974)3.0e4 (3e4)7/15
P-zero tran noiseless 2.0 (1)6.2 (6)6.5 (5)6.7 (3)11 (5)906 (1230)3.2e4 (5e4)1/15
PRCGA sawyerr noiseless 2.1 (2)2.4 (3)6.0 (4)13 (2)24 (37)199 (287)1047 (1951)7/15
SMAC-BBOB hutter noiseless 1.1 (0.2)1.9 (1)2.7 (1)4.4 (1)12 (17)2000/15
U-DCN tran noiseless 2.0 (1)3.2 (6)10 (5)87 (227)2038 (5657)8.9e4 (8e4)2e60/15
U-zero tran noiseless 2.0 (2)2.5 (2)12 (4)238 (536)4571 (8611)2.1e5 (2e5)2e60/15
fmincon pal noiseless 2.7 (2)1.1 (0.8)1.0 (0.5)1.0 (0.5)0.93 (0.4)1.1 (0.2)473 (351)1/15
fminunc pal noiseless 2.2 (2)1.8 (2)1.5 (1)1.4 (0.8)1.2 (0.6)1.0 (0.4)241 (525)5/15
lmm-CMA-ES auger noiseless 1.3 (0)1.9 (1)1.9 (0.5)2.1 (0.6)2.1 (0.5)2.1 (0.3)2.3 (0.4)15/15
simplex pal noiseless 11 (0)8.4 (7)4.8 (0.9)4.0 (0.8)2.9 (0.6)2.1 (0.3)1.8 (0.3)15/15
tany liao noiseless 2.3 (4)2.1 (2)3.3 (1)4.2 (0.8)5.9 (2)7.5 (0.7)7.8 (0.9)15/15
texp liao noiseless 4.1 (6)2.6 (2)2.7 (2)4.1 (2)5.4 (2)7.8 (1.0)7.8 (0.9)15/15

Δ fopt
f15, 2-D
1e1
37
1e0
291
1e-1
1033
1e-2
1066
1e-3
1113
1e-5
1231
1e-7
1412
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.4 (2)2.6 (2)2.3 (2)2.9 (2)3.3 (4)3.1 (3)2.8 (5)15/15
BIPOP-saACM-k loshchilov noiseless 1.1 (0.8)1.3 (1)2.3 (3)2.3 (2)2.3 (2)2.1 (2)1.9 (2)15/15
CGA-grid100 holtschulte noiseless 2.7 (5)18 (21)42 (108)166 (160)607 (809)1e50/15
CGA-grid16 holtschulte noiseless 4.7 (4)13 (12)24 (20)42 (23)95 (119)1218 (995)1e50/15
CGA-ring100 holtschulte noiseless 3.1 (3)11 (8)9.0 (5)38 (20)116 (189)1215 (2600)1e50/15
CGA-ring16 holtschulte noiseless 3.1 (2)25 (10)15 (11)31 (17)67 (80)1192 (1523)1e50/15
CMAES Hutter hutter noiseless 0.99 (0.9)2.5 (4)2.9 (2)2060/15
DE Pal pal noiseless 1.6 (1)2.2 (1)6.8 (10)6.8 (28)6.7 (9)6.2 (0.3)5.5 (7)13/15
GA-100 holtschulte noiseless 2.7 (3)9.3 (13)9.0 (4)48 (69)182 (222)1e50/15
HCMA loshchilov noiseless 1.1 (0.4)1.7 (1)1.7 (2)1.7 (2)1.7 (1)1.6 (1)1.4 (2)15/15
HILL holtschulte noiseless 2.6 (1)42 (27)19 (28)27 (19)67 (89)595 (526)1e50/15
HMLSL pal noiseless 3.0 (1)1.4 (1)5.2 (19)5.1 (10)4.9 (21)4.4 (15)3.9 (7)14/15
IP-10DDr liao noiseless 1.1 (0.5)2.8 (2)3.2 (4)3.4 (4)3.3 (4)3.1 (3)2.8 (4)15/15
IP-500 liao noiseless 1.1 (0.6)2.7 (7)2.8 (4)3.2 (3)3.1 (4)2.9 (2)2.7 (2)15/15
IPOP400D auger noiseless 0.95 (1)2.4 (2)1.6 (1)1.6 (0.5)1.5 (1)1.4 (2)1.3 (1)9/15
IP liao noiseless 1.1 (0.5)2.7 (4)2.8 (4)3.2 (3)3.1 (3)2.9 (3)2.7 (2)15/15
MEMPSODE voglis noiseless 1.6 (1)4.8 (2)6.6 (6)6.4 (7)6.4 (4)5.9 (10)6.3 (9)15/15
MLSL pal noiseless 2.6 (2)1.7 (1)2.0 (1)1.9 (1)1.8 (3)1.7 (2)1.4 (1)15/15
OQNLP pal noiseless 4.6 (1)1.3 (1.0)0.91 (0.4)0.89 (1)0.86 (1)0.79 (0.2)0.91 (0.9)14/15
P-DCN tran noiseless 5.8 (11)1279 (3437)1788 (1455)1733 (2046)1660 (3140)1504 (1668)1316 (1861)8/15
P-zero tran noiseless 4.9 (11)827 (3064)3455 (5819)3348 (2488)3209 (3707)2913 (3352)2568 (3512)5/15
PRCGA sawyerr noiseless 1.4 (1)2.8 (4)8.7 (11)8.9 (9)8.9 (9)9.2 (8)9.0 (10)15/15
SMAC-BBOB hutter noiseless 1.4 (1)1.9 (2)2000/15
U-DCN tran noiseless 2.0 (3)24 (30)71 (130)72 (89)85 (143)479 (744)5862 (5102)1/15
U-zero tran noiseless 1.4 (1)69 (153)43 (40)54 (50)100 (51)546 (553)1.0e4 (2e4)1/15
fmincon pal noiseless 3.3 (2)1.6 (2)1.2 (2)1.2 (2)1.1 (1.0)1.0 (0.4)0.91 (1)15/15
fminunc pal noiseless 3.0 (3)1.5 (3)2.8 (2)2.8 (2)2.6 (3)2.4 (2)2.1 (2)15/15
lmm-CMA-ES auger noiseless 0.75 (0.5)1.2 (1)0.72 (0.6)0.82 (1)0.80 (0.8)0.74 (0.5)0.71 (1)12/15
simplex pal noiseless 4.8 (2)3.5 (6)4.3 (4)4.2 (4)4.0 (2)3.7 (4)3.2 (4)15/15
tany liao noiseless 0.92 (0.7)2.9 (2)2.6 (1.0)2.7 (0.9)2.7 (1.0)2.5 (1)2.3 (0.7)15/15
texp liao noiseless 1.1 (0.5)3.6 (4)4.0 (5)4.6 (4)4.5 (5)4.2 (5)3.7 (4)15/15

Δ fopt
f16, 2-D
1e1
9.0
1e0
50
1e-1
174
1e-2
326
1e-3
358
1e-5
409
1e-7
538
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.8 (1)4.5 (5)3.9 (5)2.5 (3)2.6 (3)2.5 (4)2.1 (2)15/15
BIPOP-saACM-k loshchilov noiseless 3.1 (3)2.7 (1)1.6 (2)1.2 (1)1.2 (1)1.6 (0.5)1.5 (2)15/15
CGA-grid100 holtschulte noiseless 2.7 (2)2.3 (3)25 (20)244 (228)631 (844)3559 (3484)1e50/15
CGA-grid16 holtschulte noiseless 2.9 (4)11 (3)29 (71)97 (90)455 (289)1e50/15
CGA-ring100 holtschulte noiseless 3.7 (3)7.9 (7)21 (22)47 (45)147 (97)1058 (1052)1e50/15
CGA-ring16 holtschulte noiseless 2.7 (2)5.2 (3)15 (34)73 (30)322 (415)816 (769)2747 (3392)0/15
CMAES Hutter hutter noiseless 4.1 (4)3.1 (3)2.3 (4)4.6 (6)4.2 (4)2060/15
DE Pal pal noiseless 2.6 (4)5.8 (10)5.1 (2)5.2 (4)6.0 (3)6.0 (2)5.0 (2)15/15
GA-100 holtschulte noiseless 2.3 (2)4.4 (6)11 (12)146 (184)604 (1000)3475 (5379)1e50/15
HCMA loshchilov noiseless 3.0 (3)7.3 (9)4.6 (9)2.9 (2)2.9 (4)2.9 (1)2.5 (1)15/15
HILL holtschulte noiseless 2.9 (3)10 (15)29 (49)76 (140)330 (440)1e50/15
HMLSL pal noiseless 8.1 (6)5.7 (4)5.4 (4)10 (6)31 (63)34 (30)29 (35)14/15
IP-10DDr liao noiseless 2.5 (2)3.1 (10)6.2 (3)4.7 (5)4.4 (4)4.1 (4)3.3 (3)15/15
IP-500 liao noiseless 2.5 (5)3.1 (6)6.2 (9)4.7 (4)4.4 (4)4.1 (4)3.3 (3)15/15
IPOP400D auger noiseless 2.7 (4)3.7 (8)4.0 (5)2.9 (4)3.0 (2)3.1 (5)2.8 (4)9/15
IP liao noiseless 2.5 (1)3.1 (1)6.2 (9)4.7 (5)4.4 (3)4.1 (4)3.3 (2)15/15
MEMPSODE voglis noiseless 3.8 (4)10 (14)8.8 (7)6.9 (3)6.4 (5)11 (15)11 (8)15/15
MLSL pal noiseless 9.2 (8)10 (10)7.0 (7)18 (22)108 (49)847 (744)2e40/15
OQNLP pal noiseless 16 (13)12 (10)10 (15)13 (16)37 (66)37440/15
P-DCN tran noiseless 4.1 (2)2861 (1e4)1770 (2874)946 (3068)1400 (2795)1275 (1226)2560 (3333)9/15
P-zero tran noiseless 3.4 (4)4601 (2e4)1793 (8626)958 (1569)876 (2797)1047 (1796)8255 (1e4)3/15
PRCGA sawyerr noiseless 3.7 (6)8.7 (3)10 (53)10 (23)22 (83)28 (36)25 (39)15/15
SMAC-BBOB hutter noiseless 1.9 (1)1.9 (4)3.9 (2)2000/15
U-DCN tran noiseless 2.6 (2)3.4 (3)9.2 (13)28 (29)407 (1306)1.4e4 (1e4)1.5e4 (1e4)3/15
U-zero tran noiseless 2.4 (4)4.2 (3)19 (18)123 (411)875 (1396)8867 (3447)2e60/15
fmincon pal noiseless 9.1 (15)7.3 (9)9.5 (14)15 (56)113 (104)422 (1162)2e40/15
fminunc pal noiseless 13 (8)12 (19)20 (14)35 (15)112 (102)2e40/15
lmm-CMA-ES auger noiseless 2.4 (1)2.4 (3)1.9 (5)1.5 (2)1.5 (1)1.4 (0.5)1.1 (1)14/15
simplex pal noiseless 15 (2)5.8 (5)4.0 (4)2.8 (3)2.8 (1)3.1 (2)2.6 (3)15/15
tany liao noiseless 1.7 (3)2.8 (3)3.9 (3)2.4 (2)2.3 (1)2.3 (2)2.1 (2)15/15
texp liao noiseless 2.4 (2)6.6 (10)3.5 (4)2.9 (3)2.9 (2)2.8 (2)2.3 (2)15/15

Δ fopt
f17, 2-D
1e1
3.0
1e0
61
1e-1
133
1e-2
275
1e-3
396
1e-5
1086
1e-7
1657
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.3 (5)2.0 (5)1.6 (1)1.2 (0.4)1.5 (1.0)1.3 (0.5)1.0 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 9.2 (2)1.7 (2)1.5 (0.7)1.2 (0.6)1.6 (1)1.7 (1)2.0 (2)15/15
CGA-grid100 holtschulte noiseless 1.7 (3)5.1 (4)50 (61)435 (530)1787 (505)1e50/15
CGA-grid16 holtschulte noiseless 1.7 (2)3.8 (4)18 (18)194 (213)1791 (1240)1e50/15
CGA-ring100 holtschulte noiseless 2.6 (2)4.9 (7)26 (11)77 (14)1175 (1628)1e50/15
CGA-ring16 holtschulte noiseless 2.2 (3)2.1 (1)15 (15)115 (46)513 (656)1e50/15
CMAES Hutter hutter noiseless 2.8 (3)0.78 (0.7)1.1 (0.5)1.8 (2)2060/15
DE Pal pal noiseless 2.6 (3)1.6 (1.0)2.3 (0.6)1.7 (0.6)2.2 (0.6)1.4 (0.2)1.2 (0.2)15/15
GA-100 holtschulte noiseless 1.5 (1)3.2 (0.8)14 (7)254 (233)3679 (4293)1e50/15
HCMA loshchilov noiseless 2.2 (2)3.0 (5)2.4 (2)2.3 (3)2.3 (1)2.9 (2)2.7 (2)15/15
HILL holtschulte noiseless 3.6 (8)1.9 (0.7)15 (32)122 (25)659 (635)1e50/15
HMLSL pal noiseless 10 (18)17 (25)19 (16)15 (7)13 (8)9.4 (10)7.0 (0.6)14/15
IP-10DDr liao noiseless 2.1 (2)5.0 (4)3.3 (3)1.9 (1)1.8 (1)1.2 (0.5)0.95 (0.4)15/15
IP-500 liao noiseless 2.1 (1)5.0 (6)3.3 (3)1.9 (0.9)1.8 (1)1.2 (0.5)0.95 (0.4)15/15
IPOP400D auger noiseless 1.7 (1)1.7 (0.6)2.6 (2)1.8 (2)1.8 (1)1.5 (0.1)7.3 (12)0/15
IP liao noiseless 2.1 (2)5.0 (7)3.3 (3)1.9 (2)1.8 (1)1.2 (0.3)0.95 (0.3)15/15
MEMPSODE voglis noiseless 2.1 (1)2.3 (2)5.7 (13)7.5 (8)7.1 (6)8.1 (6)6.4 (4)15/15
MLSL pal noiseless 11 (12)58 (55)68 (35)307 (270)1199 (857)3e40/15
OQNLP pal noiseless 22 (24)3.5 (0.8)7.0 (3)10 (8)70 (49)53 (16)39360/15
P-DCN tran noiseless 6.2 (17)9.1 (12)5.4 (6)4.2 (3)18 (14)2320 (4321)1534 (2428)6/15
P-zero tran noiseless 2.3 (5)27 (62)15 (28)10 (16)43 (58)6166 (7954)2e60/15
PRCGA sawyerr noiseless 1.4 (2)0.96 (0.8)4.1 (4)11 (11)10 (12)7.9 (12)6.0 (4)15/15
SMAC-BBOB hutter noiseless 1.3 (0.8)1.8 (2)22 (15)2000/15
U-DCN tran noiseless 2.6 (3)3.3 (4)36 (95)2896 (3655)3141 (3830)2e60/15
U-zero tran noiseless 2.3 (3)3.3 (6)15 (27)1164 (2093)3257 (3114)2e60/15
fmincon pal noiseless 10 (13)31 (29)89 (40)410 (296)3e40/15
fminunc pal noiseless 4.7 (4)4.8 (4)26 (25)236 (545)755 (651)2e40/15
lmm-CMA-ES auger noiseless 2.3 (1)0.88 (1)1.1 (1.0)0.83 (0.5)0.78 (0.4)1.7 (2)1.3 (1)8/15
simplex pal noiseless 16 (14)4.1 (6)13 (15)48 (141)50 (39)284 (353)186 (339)1/15
tany liao noiseless 2.7 (4)0.70 (0.4)2.5 (2)1.7 (2)1.6 (1)1.4 (0.2)1.1 (0.8)15/15
texp liao noiseless 26 (97)3.7 (3)6.0 (4)3.2 (4)2.9 (3)1.7 (0.1)1.3 (0.7)15/15

Δ fopt
f18, 2-D
1e1
19
1e0
134
1e-1
666
1e-2
1249
1e-3
1708
1e-5
2438
1e-7
2858
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.9 (2)3.3 (8)1.5 (0.9)1.2 (3)0.99 (1)1.1 (1)1.3 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 4.4 (1)4.5 (4)1.6 (2)1.0 (1)1.0 (0.4)1.2 (0.4)1.2 (0.5)15/15
CGA-grid100 holtschulte noiseless 2.9 (5)17 (18)118 (227)569 (460)855 (1478)1e50/15
CGA-grid16 holtschulte noiseless 2.2 (2)16 (16)84 (107)1e50/15
CGA-ring100 holtschulte noiseless 4.1 (4)11 (9)31 (21)204 (302)1e50/15
CGA-ring16 holtschulte noiseless 3.0 (3)8.0 (10)96 (106)345 (481)1e50/15
CMAES Hutter hutter noiseless 1.4 (2)1.5 (2)1.5 (1)2060/15
DE Pal pal noiseless 1.9 (1)1.9 (0.6)5.2 (0.3)3.2 (0.4)2.6 (0.2)2.2 (0.1)2.2 (7)14/15
GA-100 holtschulte noiseless 2.1 (2)8.7 (11)71 (21)250 (125)872 (951)1e50/15
HCMA loshchilov noiseless 1.5 (2)3.1 (2)1.3 (1)1.2 (1.0)1.2 (0.7)1.8 (2)2.0 (2)15/15
HILL holtschulte noiseless 2.2 (1)17 (25)59 (119)1135 (1121)1e50/15
HMLSL pal noiseless 15 (10)29 (32)10 (4)7.2 (7)6.1 (3)8.2 (10)7.7 (3)13/15
IP-10DDr liao noiseless 1.4 (0.7)7.1 (9)3.3 (4)1.9 (0.2)1.6 (1)1.3 (0.4)1.4 (1.0)15/15
IP-500 liao noiseless 1.4 (0.9)7.1 (9)3.1 (2)1.8 (0.7)1.5 (0.5)1.3 (0.1)1.4 (0.7)15/15
IPOP400D auger noiseless 1.9 (1)5.1 (9)2.7 (3)1.5 (2)1.4 (1)3.0 (2)4.0 (6)2/15
IP liao noiseless 1.4 (0.6)7.1 (9)3.1 (2)1.8 (0.8)1.5 (0.5)1.3 (0.4)1.4 (0.2)15/15
MEMPSODE voglis noiseless 4.5 (9)18 (11)8.1 (5)6.8 (3)6.6 (2)6.3 (3)7.6 (5)15/15
MLSL pal noiseless 16 (35)35 (27)53 (44)214 (233)4e40/15
OQNLP pal noiseless 7.9 (3)4.0 (2)3.2 (3)22 (12)40650/15
P-DCN tran noiseless 6.5 (4)228 (703)49 (29)32 (77)131 (244)3540 (2027)1.0e4 (1e4)1/15
P-zero tran noiseless 4.1 (4)2071 (160)421 (2257)250 (422)769 (570)2e60/15
PRCGA sawyerr noiseless 1.7 (2)14 (23)7.6 (7)15 (19)19 (22)33 (50)31 (29)7/15
SMAC-BBOB hutter noiseless 1.2 (1)3.7 (4)2000/15
U-DCN tran noiseless 2.3 (2)24 (11)252 (505)3494 (4404)7796 (4962)2e60/15
U-zero tran noiseless 2.8 (5)29 (14)204 (263)7009 (8012)2e60/15
fmincon pal noiseless 22 (9)33 (15)48 (61)406 (255)4e40/15
fminunc pal noiseless 4.2 (3)13 (9)22 (19)2e40/15
lmm-CMA-ES auger noiseless 1.8 (0.8)2.6 (3)1.1 (2)0.80 (0.8)0.87 (0.8)1.1 (0.8)0.97 (0.4)8/15
simplex pal noiseless 7.2 (3)4.7 (2)6.4 (8)34 (22)25 (45)65 (127)55 (49)2/15
tany liao noiseless 1.7 (1)6.7 (5)2.9 (2)1.9 (0.4)1.5 (0.6)1.3 (0.4)1.3 (0.5)15/15
texp liao noiseless 7.8 (3)8.8 (11)2.7 (5)1.9 (1)1.5 (0.9)1.4 (0.5)1.6 (0.8)15/15

Δ fopt
f19, 2-D
1e1
1
1e0
1
1e-1
26
1e-2
216
1e-3
227
1e-5
252
1e-7
276
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.8 (5)26 (18)9.0 (10)18 (28)22 (32)31 (27)29 (8)15/15
BIPOP-saACM-k loshchilov noiseless 4.1 (4)21 (17)4.6 (8)13 (8)16 (18)17 (25)15 (8)15/15
CGA-grid100 holtschulte noiseless 3.9 (4)67 (140)22 (21)22 (17)49 (13)581 (895)5166 (4529)0/15
CGA-grid16 holtschulte noiseless 3.7 (1)42 (37)11 (12)24 (53)61 (48)360 (145)5126 (4801)1/15
CGA-ring100 holtschulte noiseless 4.1 (3)28 (46)19 (26)19 (12)38 (45)440 (641)1179 (1441)0/15
CGA-ring16 holtschulte noiseless 6.7 (6)51 (58)13 (9)20 (34)33 (34)428 (470)1644 (2393)1/15
CMAES Hutter hutter noiseless 4.3 (4)53 (55)11 (9)14 (8)13 (12)2060/15
DE Pal pal noiseless 5.5 (4)47 (14)8.5 (6)71 (93)70 (92)67 (84)62 (147)11/15
GA-100 holtschulte noiseless 6.5 (6)40 (28)15 (14)20 (14)56 (45)358 (731)1e50/15
HCMA loshchilov noiseless 5.5 (3)45 (41)10 (2)17 (7)22 (14)22 (6)21 (20)15/15
HILL holtschulte noiseless 12 (13)36 (14)10 (16)32 (66)50 (64)387 (153)1717 (750)0/15
HMLSL pal noiseless 1 (0)1 (0)0.65 (0)0.15 (0)0.18 (0)0.23 (0)0.28 (0.0)15/15
IP-10DDr liao noiseless 4.1 (4)24 (29)13 (3)15 (20)16 (20)26 (25)24 (55)15/15
IP-500 liao noiseless 4.1 (4)24 (25)13 (3)16 (31)17 (26)18 (25)17 (25)15/15
IPOP400D auger noiseless 1 (0)1 (0)3.4 (7)13 (17)16 (10)15 (22)14 (23)5/15
IP liao noiseless 4.1 (4)24 (31)13 (17)16 (12)17 (30)18 (36)17 (4)15/15
MEMPSODE voglis noiseless 7.6 (8)40 (42)14 (4)47 (77)46 (26)50 (89)49 (113)15/15
MLSL pal noiseless 1 (0)1 (0)0.65 (0)0.15 (0)0.18 (0)0.23 (0)0.28 (0.0)15/15
OQNLP pal noiseless 1 (0)1 (0)0.46 (0)8.7 (3)8.3 (5)7.5 (4)7.0 (6)11/15
P-DCN tran noiseless 4.5 (2)42 (12)11 (6)6.0e4 (5e4)5.7e4 (4e4)5.2e4 (3e4)4.7e4 (6e4)2/15
P-zero tran noiseless 4.5 (2)27 (26)10 (3)1.3e5 (4e5)1.2e5 (1e5)1.1e5 (9e4)1.0e5 (1e5)1/15
PRCGA sawyerr noiseless 3.2 (3)30 (21)3.0 (4)11 (13)13 (17)23 (20)37 (40)15/15
SMAC-BBOB hutter noiseless 1 (0)1 (0)6.6 (6)6.5 (8)2000/15
U-DCN tran noiseless 4.6 (2)33 (35)12 (16)53 (48)156 (155)560 (317)1.0e4 (7534)2/15
U-zero tran noiseless 4.5 (2)36 (36)11 (12)117 (193)213 (260)2214 (2733)1.0e5 (9e4)0/15
fmincon pal noiseless 1 (0)1 (0)0.65 (0)0.15 (0)0.18 (0)0.23 (0)0.28 (0.0)15/15
fminunc pal noiseless 1 (0)1 (0)0.56 (0.1)8.9 (7)8.6 (7)7.8 (6)7.2 (8)15/15
lmm-CMA-ES auger noiseless 1 (0)1 (0)5.2 (12)6.1 (3)6.7 (8)6.9 (7)7.2 (11)8/15
simplex pal noiseless 1 (0)1 (0)0.34 (0.0)9.2 (9)8.8 (5)8.1 (5)7.4 (6)15/15
tany liao noiseless 2.8 (2)19 (22)28 (37)26 (44)30 (39)28 (24)26 (34)15/15
texp liao noiseless 3.6 (6)15 (16)21 (39)12 (14)15 (17)15 (10)14 (15)15/15

Δ fopt
f20, 2-D
1e1
4.0
1e0
61
1e-1
365
1e-2
366
1e-3
366
1e-5
370
1e-7
375
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.9 (2)11 (5)10 (10)10 (11)12 (10)12 (10)12 (9)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (2)6.0 (6)5.5 (10)6.2 (7)8.0 (10)8.0 (8)7.9 (8)15/15
CGA-grid100 holtschulte noiseless 2.7 (2)19 (17)37 (44)162 (50)566 (576)1e50/15
CGA-grid16 holtschulte noiseless 1.9 (2)7.3 (8)34 (109)81 (144)105 (122)951 (565)1e50/15
CGA-ring100 holtschulte noiseless 1.9 (2)16 (10)7.6 (5)21 (20)67 (12)464 (549)1e50/15
CGA-ring16 holtschulte noiseless 4.0 (4)5.3 (4)3.7 (0.7)8.2 (7)26 (24)245 (215)3993 (3467)0/15
CMAES Hutter hutter noiseless 2.0 (2)4.6 (4)3.9 (3)4.0 (5)4.1 (5)8.3 (8)2060/15
DE Pal pal noiseless 2.8 (2)51 (166)74 (55)75 (109)75 (109)75 (162)74 (80)9/15
GA-100 holtschulte noiseless 2.0 (3)8.2 (4)5.5 (4)14 (13)63 (36)1254 (1333)1e50/15
HCMA loshchilov noiseless 1.6 (0.7)6.1 (7)8.9 (5)10 (16)12 (6)12 (14)13 (6)15/15
HILL holtschulte noiseless 5.0 (5)6.3 (10)33 (129)37 (85)55 (38)309 (375)3956 (3400)0/15
HMLSL pal noiseless 2.0 (0)5.5 (3)1.7 (0.4)2.0 (0.6)2.0 (4)2.0 (1)2.0 (1)15/15
IP-10DDr liao noiseless 2.9 (3)17 (45)21 (14)21 (14)21 (14)21 (14)21 (13)15/15
IP-500 liao noiseless 2.9 (3)13 (30)14 (6)15 (6)20 (5)22 (6)22 (9)15/15
IPOP400D auger noiseless 1.8 (2)18 (30)29 (26)62 (56)62 (101)62 (76)61 (64)1/15
IP liao noiseless 2.9 (3)13 (30)14 (4)15 (6)20 (5)22 (6)22 (5)15/15
MEMPSODE voglis noiseless 3.6 (2)8.5 (7)2.8 (4)2.9 (3)3.1 (3)3.3 (3)4.7 (3)15/15
MLSL pal noiseless 2.0 (0)6.4 (3)2.8 (3)2.8 (3)2.8 (3)2.8 (2)2.8 (3)15/15
OQNLP pal noiseless 3.2 (0)12 (7)4.0 (1)4.0 (2)4.0 (1)4.0 (2)4.0 (2)15/15
P-DCN tran noiseless 4.2 (4)2.0e4 (2e4)6880 (7690)6861 (5464)6862 (4936)6791 (5475)6706 (8037)7/15
P-zero tran noiseless 4.7 (5)4.9e4 (5e4)8241 (8240)8218 (9552)8218 (5486)8145 (5408)8111 (7998)6/15
PRCGA sawyerr noiseless 1.6 (1)17 (13)23 (28)24 (43)25 (17)28 (27)31 (14)15/15
SMAC-BBOB hutter noiseless 0.98 (0.9)2.7 (4)2000/15
U-DCN tran noiseless 1.8 (1)5.8 (3)3.6 (3)5.8 (7)13 (19)44 (80)1085 (1195)3/15
U-zero tran noiseless 2.5 (2)13 (21)14 (15)23 (24)44 (16)283 (149)1.2e4 (2e4)5/15
fmincon pal noiseless 2.0 (0)4.7 (2)2.5 (2)2.5 (1)2.5 (3)2.5 (3)2.5 (3)15/15
fminunc pal noiseless 1.8 (0)7.8 (5)2.7 (2)2.7 (3)2.8 (2)2.7 (4)2.7 (2)15/15
lmm-CMA-ES auger noiseless 1.9 (1)14 (22)14 (21)15 (18)15 (38)15 (22)15 (13)4/15
simplex pal noiseless 8.3 (0.1)14 (10)4.7 (4)4.7 (4)4.8 (4)4.7 (4)4.7 (4)15/15
tany liao noiseless 1.1 (0.9)19 (28)15 (14)16 (13)16 (12)17 (14)17 (12)15/15
texp liao noiseless 2.2 (2)20 (15)11 (14)18 (33)23 (27)23 (27)23 (32)15/15

Δ fopt
f21, 2-D
1e1
2.0
1e0
51
1e-1
174
1e-2
276
1e-3
290
1e-5
324
1e-7
330
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (0.8)4.8 (12)6.4 (6)4.1 (7)6.3 (9)5.8 (6)5.9 (6)15/15
BIPOP-saACM-k loshchilov noiseless 1.2 (0.8)7.6 (7)5.2 (9)3.5 (6)3.4 (5)3.2 (4)3.2 (4)15/15
CGA-grid100 holtschulte noiseless 0.93 (1)1.2 (2)2.0 (2)4.4 (5)7.1 (6)46 (28)173 (134)9/15
CGA-grid16 holtschulte noiseless 0.90 (0.2)1.4 (0.9)13 (0.6)10 (24)14 (1)38 (106)91 (152)13/15
CGA-ring100 holtschulte noiseless 1.5 (0.6)1.3 (1)1.7 (2)2.2 (2)3.9 (3)15 (10)80 (48)14/15
CGA-ring16 holtschulte noiseless 0.93 (0.9)3.1 (6)1.8 (2)2.1 (1)3.2 (5)14 (6)55 (72)13/15
CMAES Hutter hutter noiseless 1.0 (0.6)2.0 (0.6)0.99 (0.8)1.4 (2)1.4 (1)2.1 (4)2.9 (4)3/15
DE Pal pal noiseless 1.7 (1)1.6 (1)58 (116)37 (73)36 (69)32 (62)32 (91)12/15
GA-100 holtschulte noiseless 0.83 (0.5)1.8 (0.4)1.6 (2)2.0 (2)3.5 (3)14 (9)32 (19)15/15
HCMA loshchilov noiseless 1.7 (2)3.7 (4)5.8 (15)3.8 (2)6.1 (4)7.4 (9)7.4 (5)15/15
HILL holtschulte noiseless 1.4 (1)11 (11)98 (6)62 (93)59 (93)59 (84)107 (68)12/15
HMLSL pal noiseless 1.9 (2)2.1 (3)1.4 (0.9)0.94 (1.0)1.0 (1)0.97 (0.2)1.0 (0.6)15/15
IP-10DDr liao noiseless 2.2 (2)7.3 (8)12 (14)13 (10)14 (27)17 (30)16 (7)15/15
IP-500 liao noiseless 2.2 (2)7.3 (8)13 (24)13 (10)41 (7)126 (146)557 (318)13/15
IPOP400D auger noiseless 1.2 (0.8)6.3 (5)3.7 (4)2.5 (3)2.4 (6)2.3 (2)2.4 (2)12/15
IP liao noiseless 2.2 (2)7.3 (11)13 (9)13 (22)74 (397)126 (382)570 (266)14/15
MEMPSODE voglis noiseless 1.6 (2)1.7 (2)1.8 (3)1.3 (2)1.4 (2)1.4 (2)2.1 (1)15/15
MLSL pal noiseless 1.9 (2)1.4 (1)1.1 (0.6)0.68 (1)0.69 (1.0)0.68 (0.9)0.75 (0.6)15/15
OQNLP pal noiseless 3.6 (4)2.0 (2)0.97 (0.8)0.70 (0.3)0.76 (0.5)0.74 (0.1)0.85 (0.2)15/15
P-DCN tran noiseless 1.1 (1)3.4e4 (5e4)1.3e4 (2e4)8282 (2e4)7882 (1e4)7056 (9260)6928 (1e4)7/15
P-zero tran noiseless 1.1 (1)4.5e4 (2e4)1.3e4 (2e4)8360 (2e4)7956 (2e4)7122 (9259)6993 (1e4)7/15
PRCGA sawyerr noiseless 1.4 (2)6.9 (2)9.0 (10)6.0 (1)6.5 (9)7.1 (8)9.3 (29)15/15
SMAC-BBOB hutter noiseless 0.77 (0.5)1.2 (0.6)0.49 (0.3)0.49 (0.4)0.79 (1)8.9 (12)2000/15
U-DCN tran noiseless 1.1 (0.5)0.56 (0.5)0.49 (0.2)1.4 (2)2.6 (4)12 (23)35 (44)15/15
U-zero tran noiseless 1.1 (0.5)0.73 (0.3)1.5 (2)3.6 (3)8.3 (6)23 (50)132 (65)15/15
fmincon pal noiseless 1.9 (2)1.4 (1)0.78 (1)0.60 (1)0.59 (0.3)0.58 (0.3)0.65 (0.2)15/15
fminunc pal noiseless 2.5 (2)1.4 (0.5)0.62 (0.3)0.44 (0.2)0.53 (0.2)0.54 (0.1)0.59 (0.1)15/15
lmm-CMA-ES auger noiseless 0.83 (0.8)1.5 (2)2.7 (3)1.8 (3)1.7 (3)1.8 (4)1.8 (0.4)12/15
simplex pal noiseless 13 (23)3.3 (0.9)1.3 (0.5)0.84 (0.4)0.82 (0.5)0.77 (0.4)0.78 (0.4)15/15
tany liao noiseless 1.8 (2)10 (17)10 (12)12 (18)13 (15)12 (5)12 (19)15/15
texp liao noiseless 2.2 (2)14 (4)18 (8)12 (12)11 (15)10 (12)10 (11)15/15

Δ fopt
f22, 2-D
1e1
5.0
1e0
27
1e-1
168
1e-2
218
1e-3
249
1e-5
289
1e-7
306
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.2 (2)5.8 (10)4.3 (3)3.5 (7)3.3 (2)3.3 (1)3.2 (1)15/15
BIPOP-saACM-k loshchilov noiseless 1.9 (4)9.1 (6)5.9 (9)5.6 (7)5.4 (6)5.5 (6)5.2 (5)15/15
CGA-grid100 holtschulte noiseless 0.92 (1)2.2 (2)2.8 (3)8.8 (11)21 (20)77 (66)393 (234)5/15
CGA-grid16 holtschulte noiseless 1.2 (0.6)3.7 (3)2.0 (2)4.5 (7)10 (17)33 (40)281 (211)8/15
CGA-ring100 holtschulte noiseless 1.1 (0.5)2.9 (0.9)2.4 (3)4.3 (4)8.4 (7)43 (33)104 (109)10/15
CGA-ring16 holtschulte noiseless 1.4 (0.8)5.5 (9)3.3 (2)4.5 (5)6.9 (8)41 (44)280 (533)6/15
CMAES Hutter hutter noiseless 1.5 (2)7.9 (18)3.6 (4)14 (16)12 (15)10 (8)10 (8)0/15
DE Pal pal noiseless 1.3 (0.8)3.7 (4)18 (1)14 (1.0)13 (0.9)12 (35)12 (1)14/15
GA-100 holtschulte noiseless 1.3 (2)3.0 (5)2.3 (2)7.5 (7)15 (19)74 (82)178 (134)9/15
HCMA loshchilov noiseless 2.2 (3)4.4 (7)3.5 (4)3.2 (10)3.3 (5)3.0 (2)2.9 (5)15/15
HILL holtschulte noiseless 1.6 (0.6)271 (1857)45 (152)36 (2)35 (107)66 (65)350 (815)5/15
HMLSL pal noiseless 2.9 (0.8)3.7 (3)1.2 (0.8)0.99 (0.6)0.93 (0.5)0.91 (0.4)0.93 (0.3)15/15
IP-10DDr liao noiseless 1.3 (0.8)11 (18)10 (6)23 (14)22 (7)33 (104)31 (49)15/15
IP-500 liao noiseless 1.3 (0.8)11 (13)8.5 (12)10 (16)13 (6)402 (1455)492 (1701)13/15
IPOP400D auger noiseless 1.2 (2)8.1 (12)3.3 (4)4.9 (6)4.3 (5)4.4 (6)4.3 (3)10/15
IP liao noiseless 1.3 (1)11 (11)8.5 (10)10 (11)13 (10)265 (353)1021 (4904)13/15
MEMPSODE voglis noiseless 1.8 (2)2.8 (2)2.3 (7)2.9 (5)2.9 (1)5.2 (6)10 (11)15/15
MLSL pal noiseless 2.8 (4)2.8 (2)0.96 (1.0)0.81 (0.5)0.76 (0.7)0.73 (0.8)0.78 (0.5)15/15
OQNLP pal noiseless 3.4 (2)4.2 (4)1.4 (1)1.2 (0.4)1.1 (0.3)1.0 (0.7)1.3 (0.4)14/15
P-DCN tran noiseless 2.0 (2)1.2e4 (4e4)1.1e4 (1e4)8112 (2e4)7103 (1e4)6122 (1e4)5786 (3357)8/15
P-zero tran noiseless 1.9 (0.8)1.4e4 (3e4)1.1e4 (1e4)8619 (1e4)7547 (1e4)6505 (8652)6146 (7374)8/15
PRCGA sawyerr noiseless 0.89 (1)1.9 (3)4.3 (4)13 (30)20 (12)27 (9)41 (52)15/15
SMAC-BBOB hutter noiseless 1.5 (2)1.1 (1)0.91 (0.4)0.91 (0.6)1.3 (3)10 (18)2000/15
U-DCN tran noiseless 1.3 (2)3.1 (3)1.3 (1)2.3 (5)8.1 (13)29 (32)272 (124)14/15
U-zero tran noiseless 1.2 (2)3.8 (9)2.4 (0.3)5.3 (3)13 (21)61 (39)695 (905)13/15
fmincon pal noiseless 2.9 (6)3.8 (3)0.87 (0.7)0.70 (0.5)0.67 (0.3)0.66 (0.2)0.71 (0.2)15/15
fminunc pal noiseless 2.3 (1)2.9 (2)0.88 (1)0.76 (0.4)0.77 (0.3)0.74 (0.6)0.77 (0.2)15/15
lmm-CMA-ES auger noiseless 1.5 (1)3.7 (7)2.5 (2)3.2 (3)3.1 (1)3.0 (6)2.9 (5)12/15
simplex pal noiseless 12 (12)7.0 (6)1.5 (0.8)1.2 (0.6)1.1 (0.7)1.00 (0.1)0.98 (0.2)15/15
tany liao noiseless 1.5 (0.4)3.1 (5)5.9 (4)9.1 (21)36 (22)33 (100)31 (18)15/15
texp liao noiseless 2.3 (2)21 (46)11 (13)9.2 (5)10 (15)8.9 (5)9.0 (20)15/15

Δ fopt
f23, 2-D
1e1
8.0
1e0
193
1e-1
234
1e-2
263
1e-3
299
1e-5
348
1e-7
379
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.7 (3)7.1 (8)13 (15)20 (58)18 (10)17 (26)16 (10)15/15
BIPOP-saACM-k loshchilov noiseless 1.9 (2)5.7 (8)11 (6)11 (13)11 (11)12 (10)12 (12)15/15
CGA-grid100 holtschulte noiseless 2.4 (2)10 (15)772 (670)1e50/15
CGA-grid16 holtschulte noiseless 1.6 (1)13 (8)3015 (2885)1e50/15
CGA-ring100 holtschulte noiseless 2.2 (3)11 (16)3065 (2598)1e50/15
CGA-ring16 holtschulte noiseless 1.9 (2)13 (13)1405 (746)1e50/15
CMAES Hutter hutter noiseless 1.9 (3)15 (18)2060/15
DE Pal pal noiseless 2.3 (1)3.8 (2)11 (2)14 (4)15 (3)16 (4)16 (3)15/15
GA-100 holtschulte noiseless 1.6 (2)17 (20)3047 (5961)1e50/15
HCMA loshchilov noiseless 2.4 (3)7.0 (5)14 (19)13 (17)11 (4)10 (2)10 (3)15/15
HILL holtschulte noiseless 3.3 (4)13 (16)1044 (928)1e50/15
HMLSL pal noiseless 4.4 (14)1.7 (2)2.2 (1)2.2 (2)2.2 (1)35 (29)49 (8)15/15
IP-10DDr liao noiseless 1.7 (1)6.7 (13)14 (14)13 (15)12 (7)11 (14)10 (8)15/15
IP-500 liao noiseless 1.7 (2)6.7 (14)14 (13)13 (15)12 (10)11 (10)10 (9)15/15
IPOP400D auger noiseless 2.2 (2)14 (27)23 (20)21 (13)25 (14)32 (74)30 (44)2/15
IP liao noiseless 1.7 (1)6.7 (13)14 (17)13 (18)12 (16)11 (9)10 (13)15/15
MEMPSODE voglis noiseless 1.6 (2)4.7 (9)14 (15)14 (16)13 (11)18 (17)18 (15)15/15
MLSL pal noiseless 4.4 (8)1.5 (1)1.9 (1.0)2.4 (1)2.6 (4)90 (47)3e40/15
OQNLP pal noiseless 8.9 (12)2.7 (0.9)5.1 (7)12 (10)87 (120)62970/15
P-DCN tran noiseless 1.7 (1)4.1 (2)53 (57)3382 (7087)7037 (1e4)7802 (1e4)3.6e4 (6e4)1/15
P-zero tran noiseless 1.1 (0.8)6.9 (9)312 (1230)5464 (2513)2.2e4 (3e4)2e60/15
PRCGA sawyerr noiseless 2.4 (3)5.4 (3)30 (34)60 (27)65 (193)75 (103)100 (63)14/15
SMAC-BBOB hutter noiseless 1.9 (3)15 (11)2000/15
U-DCN tran noiseless 1.6 (2)10 (7)920 (1102)2.4e4 (2e4)2e60/15
U-zero tran noiseless 1.7 (2)13 (11)2381 (3100)3.4e4 (4e4)2e60/15
fmincon pal noiseless 4.4 (5)2.0 (2)3.3 (3)3.6 (3)4.0 (5)85 (73)3e40/15
fminunc pal noiseless 5.0 (5)3.9 (4)37 (37)287 (298)571 (1083)2e40/15
lmm-CMA-ES auger noiseless 2.1 (1)3.0 (2)4.0 (5)3.6 (2)3.3 (1)3.0 (3)2.9 (3)12/15
simplex pal noiseless 22 (14)1.7 (0.9)1.5 (0.3)1.4 (0.6)1.3 (0.2)1.2 (0.6)1.2 (0.4)15/15
tany liao noiseless 2.3 (2)6.7 (11)13 (13)12 (14)11 (16)10 (10)11 (6)15/15
texp liao noiseless 2.0 (2)5.2 (5)18 (19)17 (21)15 (18)14 (17)14 (7)15/15

Δ fopt
f24, 2-D
1e1
18
1e0
857
1e-1
8515
1e-2
23399
1e-3
24113
1e-5
24721
1e-7
24721
#succ
5/15
BIPOP-aCMA-STEP loshchilov noiseless 2.6 (5)10 (16)12 (28)16 (25)24 (16)24 (31)24 (28)15/15
BIPOP-saACM-k loshchilov noiseless 1.8 (1)10 (24)15 (71)14 (17)14 (11)14 (11)14 (14)15/15
CGA-grid100 holtschulte noiseless 2.2 (3)38 (31)79 (66)1e50/15
CGA-grid16 holtschulte noiseless 1.8 (2)172 (116)166 (317)62 (77)1e50/15
CGA-ring100 holtschulte noiseless 2.2 (3)12 (9)19 (18)1e50/15
CGA-ring16 holtschulte noiseless 3.2 (3)70 (105)82 (116)1e50/15
CMAES Hutter hutter noiseless 2.8 (0.9)1.7 (2)2060/15
DE Pal pal noiseless 1.3 (2)71 (70)13 (12)6.9 (3)6.7 (10)6.6 (6)6.6 (13)3/15
GA-100 holtschulte noiseless 1.5 (2)232 (386)165 (252)1e50/15
HCMA loshchilov noiseless 1.5 (2)8.5 (23)25 (58)31 (32)35 (57)39 (32)39 (38)13/15
HILL holtschulte noiseless 2.1 (2)189 (97)78 (103)61 (79)59 (83)1e50/15
HMLSL pal noiseless 2.7 (2)2.0 (2)1.3 (1.0)2.0 (5)2.0 (2)1.9 (2)1.9 (2)7/15
IP-10DDr liao noiseless 1.7 (1)185 (323)338 (366)261 (272)362 (672)353 (769)353 (289)3/15
IP-500 liao noiseless 1.7 (2)1588 (2265)2e60/15
IPOP400D auger noiseless 1.6 (2)3.5 (4)16010/15
IP liao noiseless 1.7 (2)2034 (5554)2e60/15
MEMPSODE voglis noiseless 2.2 (2)21 (41)2.6 (5)1.3 (1)1.2 (2)1.2 (2)1.5 (2)15/15
MLSL pal noiseless 2.5 (1)2.4 (7)3.5 (5)2.4 (1)2.4 (3)2.3 (3)2.3 (4)5/15
OQNLP pal noiseless 9.1 (2)3.7 (5)2.0 (2)0.74 (0.7)0.72 (0.7)0.71 (1)0.75 (0.5)4/15
P-DCN tran noiseless 1.5 (2)4668 (5834)470 (999)172 (300)167 (249)163 (223)171 (196)4/15
P-zero tran noiseless 12 (1)4669 (2335)472 (530)173 (149)170 (314)243 (391)568 (697)1/15
PRCGA sawyerr noiseless 1.3 (1)11 (17)4.8 (6)3.8 (2)3.7 (5)3.7 (4)3.8 (4)11/15
SMAC-BBOB hutter noiseless 1.8 (2)2000/15
U-DCN tran noiseless 1.5 (1)13 (10)138 (134)286 (608)1165 (975)2e60/15
U-zero tran noiseless 1.4 (0.9)11 (9)191 (114)557 (492)1167 (1140)2e60/15
fmincon pal noiseless 2.2 (2)2.2 (3)3.6 (5)4.4 (5)4.3 (4)4.2 (5)4.2 (4)3/15
fminunc pal noiseless 3.2 (2)2.0 (1)3.1 (3)6.5 (5)6.3 (8)6.1 (9)6.1 (11)2/15
lmm-CMA-ES auger noiseless 1.6 (2)1.5 (2)16110/15
simplex pal noiseless 8.5 (3)4.1 (3)3.2 (2)7.4 (7)7.2 (9)7.0 (6)7.0 (4)2/15
tany liao noiseless 1.7 (2)85 (87)92 (102)117 (115)113 (119)110 (92)110 (72)8/15
texp liao noiseless 1.7 (0.7)4.6 (6)2.7 (4)3.5 (4)3.9 (4)3.8 (5)3.8 (4)15/15

Previous dimension | Dimension = 3 | Next dimension

Δ fopt
f1, 3-D
1e1
4.0
1e0
8.0
1e-1
8.0
1e-2
8.0
1e-3
8.0
1e-5
8.0
1e-7
8.0
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.5 (2)3.9 (0.7)4.8 (1.0)6.7 (0.2)7.4 (0.4)10 (0.4)13 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 3.1 (3)5.5 (3)10 (2)11 (0.6)12 (2)16 (3)20 (2)15/15
CGA-grid100 holtschulte noiseless 2.9 (6)41 (34)210 (63)668 (334)1634 (1224)2.3e4 (1e4)2.7e5 (2e5)0/15
CGA-grid16 holtschulte noiseless 3.7 (3)14 (9)42 (24)100 (45)311 (199)3346 (3221)4.2e4 (6e4)0/15
CGA-ring100 holtschulte noiseless 2.6 (1)40 (33)129 (57)332 (93)720 (321)3298 (844)1.8e4 (2e4)3/15
CGA-ring16 holtschulte noiseless 3.6 (1)14 (11)45 (30)107 (51)223 (83)1245 (382)1.2e4 (8310)2/15
CMAES Hutter hutter noiseless 3.6 (4)5.8 (3)14 (6)17 (3)22 (6)41 (12)283 (312)0/15
DE Pal pal noiseless 2.4 (2)10 (6)20 (9)33 (17)48 (15)74 (9)102 (10)15/15
GA-100 holtschulte noiseless 2.6 (3)25 (20)102 (35)224 (81)528 (256)3022 (2091)6.2e4 (1e5)0/15
HCMA loshchilov noiseless 1.6 (0.4)1 (0)1 (0)1 (0)★31 (0)★41 (0)★41 (0)★415/15
HILL holtschulte noiseless 5.5 (5)6.1 (4)13 (11)38 (20)162 (102)1358 (936)2.0e4 (2e4)3/15
HMLSL pal noiseless 0.98 (0.5)1.3 (0.6)1.8 (0.8)1.9 (0.5)2.3 (0.4)3.0 (0.8)3.3 (0.8)15/15
IP-10DDr liao noiseless 1.8 (2)6.0 (2)10 (3)16 (3)23 (2)35 (2)47 (2)15/15
IP-500 liao noiseless 1.8 (2)6.0 (2)10 (3)16 (4)23 (3)35 (2)47 (3)15/15
IPOP400D auger noiseless 2.4 (3)5.2 (4)11 (3)17 (5)23 (8)34 (3)45 (5)15/15
IP liao noiseless 1.8 (2)6.0 (2)10 (4)16 (4)23 (2)35 (3)47 (3)15/15
MEMPSODE voglis noiseless 2.5 (3)7.9 (2)11 (1)12 (1)14 (1)17 (1)20 (1)15/15
MLSL pal noiseless 0.98 (0.2)1.3 (0.5)1.8 (0.5)1.9 (0.5)2.3 (1)3.0 (0.2)3.3 (1)15/15
OQNLP pal noiseless 2.7 (2)1.9 (0.6)2.4 (0.9)2.7 (0.6)2.8 (0.5)2.9 (0.6)2.9 (0.7)15/15
P-DCN tran noiseless 2.9 (2)23 (16)36 (8)43 (9)55 (16)137 (52)291 (58)15/15
P-zero tran noiseless 2.2 (2)15 (7)25 (13)29 (13)38 (12)95 (32)515 (393)15/15
PRCGA sawyerr noiseless 1.4 (2)10 (9)34 (14)58 (36)163 (211)472 (1433)555 (363)15/15
SMAC-BBOB hutter noiseless 0.93 (0.6)1.3 (0.6)2.0 (0.7)3.2 (0.6)13 (8)3000/15
U-DCN tran noiseless 2.6 (3)12 (10)41 (22)102 (42)190 (132)558 (496)1305 (386)15/15
U-zero tran noiseless 2.3 (2)8.3 (5)34 (15)116 (62)327 (183)3006 (2084)3.0e4 (2e4)15/15
fmincon pal noiseless 0.98 (0.5)1.3 (0.5)1.8 (0.8)1.9 (0.5)2.3 (0.9)3.0 (1)3.3 (1)15/15
fminunc pal noiseless 1.3 (1)0.99 (0.1)1.0 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)15/15
lmm-CMA-ES auger noiseless 1.5 (1)2.3 (0.3)3.0 (2)4.1 (1.0)5.0 (0.8)6.2 (0.9)8.1 (0.5)15/15
simplex pal noiseless 10 (16)14 (11)22 (12)24 (8)26 (10)31 (6)34 (6)15/15
tany liao noiseless 2.4 (2)5.7 (2)11 (3)16 (5)23 (8)37 (5)51 (2)15/15
texp liao noiseless 2.6 (4)4.7 (3)8.4 (4)16 (6)20 (7)33 (4)45 (8)15/15

Δ fopt
f2, 3-D
1e1
38
1e0
42
1e-1
43
1e-2
44
1e-3
45
1e-5
47
1e-7
48
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.8 (0.4)2.0 (0.2)2.2 (0.4)2.4 (0.2)2.6 (0.2)2.9 (0.3)3.3 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 4.2 (0.9)4.3 (1)4.5 (0.9)4.8 (0.8)5.0 (0.6)5.5 (0.7)6.0 (0.5)15/15
CGA-grid100 holtschulte noiseless 184 (109)371 (202)1466 (929)7207 (8381)2e50/15
CGA-grid16 holtschulte noiseless 102 (162)276 (322)900 (959)4453 (3568)2.4e4 (3e4)2e50/15
CGA-ring100 holtschulte noiseless 112 (43)283 (218)1230 (577)4167 (6180)1.1e4 (2e4)2e50/15
CGA-ring16 holtschulte noiseless 53 (29)304 (232)925 (545)6294 (6130)1.1e4 (6723)2e50/15
CMAES Hutter hutter noiseless 22 (22)35 (32)3030/15
DE Pal pal noiseless 8.4 (2)11 (1)13 (1)15 (2)17 (2)21 (1)25 (1)15/15
GA-100 holtschulte noiseless 102 (31)409 (344)1714 (618)3051 (3076)8181 (9147)2e50/15
HCMA loshchilov noiseless 2.3 (2)2.9 (3)3.4 (2)3.6 (2)3.8 (2)4.1 (3)4.5 (2)15/15
HILL holtschulte noiseless 66 (126)200 (170)878 (520)1826 (1526)5929 (9389)2e50/15
HMLSL pal noiseless 1.3 (0.4)1.4 (0.4)1.5 (0.3)1.7 (0.6)1.8 (0.4)3.0 (5)5.3 (1)15/15
IP-10DDr liao noiseless 13 (5)19 (6)21 (5)22 (5)23 (4)24 (3)25 (4)15/15
IP-500 liao noiseless 13 (5)19 (7)21 (8)22 (6)23 (3)24 (4)25 (4)15/15
IPOP400D auger noiseless 10 (5)15 (6)17 (6)19 (3)19 (4)20 (2)22 (1)15/15
IP liao noiseless 13 (6)19 (8)21 (6)22 (5)23 (3)24 (3)25 (4)15/15
MEMPSODE voglis noiseless 3.8 (2)4.3 (1)4.9 (1)5.0 (1.0)5.3 (0.7)5.6 (0.4)6.0 (0.6)15/15
MLSL pal noiseless 1.3 (0.5)1.4 (0.5)1.5 (0.4)1.7 (0.3)1.8 (0.8)2.9 (0.6)4.7 (3)15/15
OQNLP pal noiseless 1.4 (0.8)1.9 (1)2.0 (0.8)2.1 (0.9)2.3 (1)2.4 (1)41 (60)5/15
P-DCN tran noiseless 13 (6)19 (24)37 (32)83 (69)177 (299)438 (461)791 (1173)15/15
P-zero tran noiseless 14 (10)23 (12)41 (15)108 (64)364 (406)2956 (4299)2.7e4 (2e4)9/15
PRCGA sawyerr noiseless 16 (6)27 (7)33 (40)171 (462)361 (75)670 (778)685 (989)15/15
SMAC-BBOB hutter noiseless 26 (45)3000/15
U-DCN tran noiseless 88 (111)156 (116)191 (294)2931 (9671)2958 (7968)3166 (1811)1.0e4 (2e4)13/15
U-zero tran noiseless 180 (401)589 (648)1363 (2433)3859 (3354)2.5e4 (5e4)4.4e5 (4e5)3e60/15
fmincon pal noiseless 1.3 (0.6)1.4 (0.2)1.5 (0.4)1.7 (0.6)1.8 (0.8)2.8 (0.6)4.6 (4)15/15
fminunc pal noiseless 2.2 (1)3.1 (1)3.9 (0.9)4.1 (2)4.3 (0.8)4.4 (0.5)4.6 (0.5)15/15
lmm-CMA-ES auger noiseless 3.2 (1)3.8 (0.5)4.1 (1)4.3 (0.8)4.3 (0.8)4.6 (0.8)4.9 (0.9)15/15
simplex pal noiseless 8.8 (6)11 (4)11 (5)11 (3)12 (4)12 (3)12 (3)15/15
tany liao noiseless 13 (5)17 (8)21 (3)22 (2)22 (2)23 (2)25 (1.0)15/15
texp liao noiseless 14 (7)20 (5)21 (1)22 (3)23 (3)24 (3)25 (3)15/15

Δ fopt
f3, 3-D
1e1
38
1e0
822
1e-1
830
1e-2
835
1e-3
842
1e-5
847
1e-7
853
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.6 (1)0.30 (0.1)0.62 (2)0.64 (1)0.66 (1)0.73 (0.1)0.77 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 3.9 (0.7)2.6 (1)13 (7)13 (16)13 (18)13 (22)15 (7)15/15
CGA-grid100 holtschulte noiseless 26 (18)10 (6)34 (24)113 (141)1309 (1478)2e50/15
CGA-grid16 holtschulte noiseless 8.3 (9)3.1 (2)8.5 (6)23 (10)66 (57)2548 (3365)2e50/15
CGA-ring100 holtschulte noiseless 25 (20)6.2 (2)13 (5)25 (8)52 (22)836 (1063)2e50/15
CGA-ring16 holtschulte noiseless 7.7 (4)2.3 (0.9)5.1 (1)14 (6)57 (16)1246 (753)2e50/15
CMAES Hutter hutter noiseless 4.0 (4)2.7 (6)5.5 (5)3030/15
DE Pal pal noiseless 4.2 (2)0.87 (0.2)6.2 (0.2)6.4 (0.3)6.4 (18)6.6 (18)6.8 (35)14/15
GA-100 holtschulte noiseless 14 (7)3.5 (1)8.5 (6)28 (7)66 (40)2e50/15
HCMA loshchilov noiseless 2.0 (1.0)0.81 (0.9)1.0 (0.6)1.0 (1)1.1 (0.6)1.1 (0.6)1.2 (0.0)15/15
HILL holtschulte noiseless 2.6 (1.0)1.1 (0.9)3.0 (2)15 (9)25 (5)640 (631)2e50/15
HMLSL pal noiseless 8.5 (1)1.4 (0.7)7.0 (37)7.1 (18)7.0 (18)7.0 (0.9)7.0 (18)14/15
IP-10DDr liao noiseless 3.3 (2)4.8 (2)18 (16)18 (13)18 (21)18 (13)18 (8)15/15
IP-500 liao noiseless 3.3 (1)5.0 (3)17 (23)20 (10)21 (39)21 (30)22 (36)15/15
IPOP400D auger noiseless 5.5 (10)2.6 (3)20070/15
IP liao noiseless 3.3 (1)5.0 (3)17 (19)47 (133)49 (260)51 (151)53 (15)15/15
MEMPSODE voglis noiseless 26 (22)3.7 (2)8.8 (7)9.4 (5)9.4 (8)10 (6)10 (7)15/15
MLSL pal noiseless 7.7 (6)6.3 (10)76 (29)75 (66)75 (93)74 (157)74 (88)6/15
OQNLP pal noiseless 10 (7)2.7 (1)10 (11)10 (14)10 (12)10 (9)10 (20)7/15
P-DCN tran noiseless 72 (18)155 (144)362 (643)360 (639)357 (188)356 (412)355 (836)15/15
P-zero tran noiseless 102 (265)115 (380)172 (40)171 (44)170 (39)176 (871)255 (545)15/15
PRCGA sawyerr noiseless 4.9 (2)2.9 (3)8.7 (6)9.0 (8)10 (10)11 (8)12 (8)15/15
SMAC-BBOB hutter noiseless 7.5 (12)5.4 (3)3000/15
U-DCN tran noiseless 5.9 (3)2.9 (2)4.2 (4)5.2 (1)7.6 (2)19 (29)391 (1037)13/15
U-zero tran noiseless 3.2 (1)2.6 (2)7.5 (8)19 (16)80 (56)618 (396)2.5e4 (3e4)0/15
fmincon pal noiseless 12 (15)8.4 (7)85 (74)85 (88)84 (56)84 (64)83 (60)6/15
fminunc pal noiseless 8.2 (5)9.1 (3)57 (94)57 (71)56 (65)56 (71)56 (16)7/15
lmm-CMA-ES auger noiseless 3.9 (5)1.5 (1)16 (21)16 (7)16 (31)16 (11)16 (28)2/15
simplex pal noiseless 15 (7)7.3 (6)106 (73)105 (149)104 (56)104 (105)103 (128)5/15
tany liao noiseless 10 (9)4.0 (5)19 (13)21 (16)21 (18)21 (20)21 (19)15/15
texp liao noiseless 12 (18)5.0 (3)14 (18)14 (7)14 (12)14 (7)14 (12)15/15

Δ fopt
f4, 3-D
1e1
40
1e0
808
1e-1
866
1e-2
921
1e-3
952
1e-5
1015
1e-7
1044
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.4 (1)7.8 (14)795 (1764)748 (876)724 (1576)679 (1478)661 (773)13/15
BIPOP-saACM-k loshchilov noiseless 6.1 (11)100 (64)2770 (1742)3358 (1435)3445 (3478)3231 (3610)3141 (5486)9/15
CGA-grid100 holtschulte noiseless 42 (24)18 (4)46 (36)121 (92)737 (794)2e50/15
CGA-grid16 holtschulte noiseless 11 (4)4.4 (2)10 (5)28 (16)86 (84)2e50/15
CGA-ring100 holtschulte noiseless 33 (15)7.8 (3)14 (3)33 (16)88 (51)2198 (3251)2e50/15
CGA-ring16 holtschulte noiseless 11 (3)2.5 (0.6)4.9 (4)15 (7)70 (90)1030 (856)2e50/15
CMAES Hutter hutter noiseless 12 (6)3030/15
DE Pal pal noiseless 6.7 (2)1.1 (0.4)26 (0.2)25 (49)24 (32)23 (15)23 (43)11/15
GA-100 holtschulte noiseless 21 (18)6.9 (3)15 (6)26 (28)90 (130)1085 (739)2e50/15
HCMA loshchilov noiseless 4.3 (7)78 (278)728 (1219)686 (331)666 (3005)626 (1479)610 (1730)13/15
HILL holtschulte noiseless 2.8 (2)1.6 (2)5.9 (8)20 (9)36 (16)1068 (865)2e50/15
HMLSL pal noiseless 8.1 (6)1.8 (1)19 (35)18 (66)18 (48)17 (30)16 (43)12/15
IP-10DDr liao noiseless 7.6 (2)55 (64)696 (678)654 (482)633 (511)594 (681)578 (556)15/15
IP-500 liao noiseless 7.6 (14)349 (341)3e60/15
IPOP400D auger noiseless 7.6 (15)17 (36)20070/15
IP liao noiseless 7.6 (1)1099 (2065)1.5e4 (7682)3e60/15
MEMPSODE voglis noiseless 12 (9)6.9 (6)14 (4)14 (7)13 (9)13 (7)13 (3)15/15
MLSL pal noiseless 11 (12)32 (43)563 (722)530 (603)513 (993)481 (633)467 (755)1/15
OQNLP pal noiseless 22 (33)13 (17)47 (30)44 (15)43 (26)40 (33)40 (53)2/15
P-DCN tran noiseless 123 (288)108 (147)198 (156)186 (205)181 (185)171 (151)199 (174)15/15
P-zero tran noiseless 709 (1595)67 (85)91 (78)86 (55)83 (72)87 (72)155 (132)15/15
PRCGA sawyerr noiseless 13 (6)8.0 (3)30 (31)29 (26)34 (33)39 (26)43 (46)14/15
SMAC-BBOB hutter noiseless 34 (28)3000/15
U-DCN tran noiseless 6.4 (4)3.5 (3)4.9 (2)8.0 (2)13 (18)48 (44)99 (251)13/15
U-zero tran noiseless 5.8 (2)2.7 (2)12 (13)45 (15)112 (105)727 (417)2.0e4 (2e4)0/15
fmincon pal noiseless 16 (14)11 (15)278 (323)261 (401)253 (220)237 (210)231 (143)2/15
fminunc pal noiseless 19 (19)21 (16)565 (878)531 (569)514 (370)482 (345)469 (680)1/15
lmm-CMA-ES auger noiseless 4.6 (7)35 (31)33 (18)31 (21)30 (22)28 (42)27 (30)1/15
simplex pal noiseless 17 (9)25 (31)145 (111)137 (270)132 (302)124 (97)121 (131)4/15
tany liao noiseless 5.6 (1)36 (46)438 (378)412 (932)398 (286)374 (588)364 (208)15/15
texp liao noiseless 11 (15)57 (98)546 (224)513 (325)600 (770)563 (895)548 (807)15/15

Δ fopt
f5, 3-D
1e1
7.0
1e0
7.0
1e-1
7.0
1e-2
7.0
1e-3
7.0
1e-5
7.0
1e-7
7.0
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.1 (0.1)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (2)4.9 (2)5.4 (2)5.4 (2)5.4 (2)5.4 (2)5.4 (2)15/15
CGA-grid100 holtschulte noiseless 29 (31)120 (80)144 (82)146 (83)146 (68)146 (94)146 (86)15/15
CGA-grid16 holtschulte noiseless 11 (12)33 (17)42 (24)43 (30)43 (25)43 (28)43 (29)15/15
CGA-ring100 holtschulte noiseless 18 (14)101 (28)121 (30)125 (27)126 (40)126 (26)126 (27)15/15
CGA-ring16 holtschulte noiseless 11 (6)26 (9)32 (11)32 (5)32 (8)32 (8)32 (7)15/15
CMAES Hutter hutter noiseless 3.7 (2)5.3 (3)5.6 (4)5.6 (2)5.6 (3)5.6 (2)5.6 (3)15/15
DE Pal pal noiseless 12 (7)46 (20)94 (20)143 (15)196 (19)298 (16)400 (27)15/15
GA-100 holtschulte noiseless 18 (18)71 (16)97 (12)98 (26)98 (24)98 (28)98 (5)15/15
HCMA loshchilov noiseless 1.1 (0)1.4 (0.2)1.5 (0.4)1.5 (0.6)1.5 (0.6)1.5 (0.3)1.5 (0.5)15/15
HILL holtschulte noiseless 4.4 (4)7.4 (5)7.6 (5)7.6 (2)7.6 (5)7.6 (5)7.6 (5)15/15
HMLSL pal noiseless 1.9 (0)3.0 (0)4.1 (0)4.1 (0)4.7 (0)4.7 (0)5.3 (0)15/15
IP-10DDr liao noiseless 2.5 (2)11 (30)13 (18)15 (9)15 (9)15 (22)15 (21)15/15
IP-500 liao noiseless 2.5 (3)11 (16)13 (18)15 (31)15 (12)15 (31)15 (7)15/15
IPOP400D auger noiseless 3.7 (2)5.8 (1)6.0 (3)6.0 (2)6.0 (3)6.0 (3)6.0 (2)15/15
IP liao noiseless 2.5 (0.6)11 (16)13 (31)15 (22)15 (17)15 (31)15 (22)15/15
MEMPSODE voglis noiseless 2.1 (2)12 (5)13 (8)13 (5)13 (4)13 (6)13 (5)15/15
MLSL pal noiseless 1.9 (0)3.0 (0)4.1 (0)4.1 (0)4.7 (0)4.7 (0)5.3 (0)15/15
OQNLP pal noiseless 2.6 (0)2.9 (0)2.9 (0)2.9 (0)2.9 (0)2.9 (0)2.9 (0)15/15
P-DCN tran noiseless 8.3 (5)65 (60)81 (42)93 (54)102 (47)130 (14)179 (39)15/15
P-zero tran noiseless 24 (37)75 (60)89 (48)95 (63)101 (51)115 (56)132 (47)15/15
PRCGA sawyerr noiseless 137 (31)2188 (1245)3756 (3817)5775 (3583)1.3e4 (1e4)2e50/15
SMAC-BBOB hutter noiseless 0.88 (0.3)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
U-DCN tran noiseless 10 (9)122 (112)453 (114)2906 (3069)5034 (2753)3.3e5 (5e5)6.3e6 (6e6)0/15
U-zero tran noiseless 7.0 (3)81 (73)773 (307)7533 (1e4)2.5e5 (2e5)3e60/15
fmincon pal noiseless 1.9 (0)3.0 (0)4.1 (0)4.1 (0)4.7 (0)4.7 (0)5.3 (0)15/15
fminunc pal noiseless 1.3 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)15/15
lmm-CMA-ES auger noiseless 2.6 (2)4.0 (1)4.1 (2)4.1 (1)4.1 (1)4.1 (2)4.1 (1)15/15
simplex pal noiseless 15 (10)41 (49)41 (47)41 (50)41 (46)41 (47)41 (49)15/15
tany liao noiseless 3.1 (1)6.4 (3)7.4 (7)7.7 (4)7.7 (7)7.7 (6)7.7 (5)15/15
texp liao noiseless 9.4 (8)27 (20)33 (31)37 (31)37 (27)38 (26)38 (31)15/15

Δ fopt
f6, 3-D
1e1
34
1e0
56
1e-1
90
1e-2
117
1e-3
149
1e-5
215
1e-7
265
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.7 (2)3.2 (0.4)3.2 (1)3.1 (0.4)3.1 (0.3)2.9 (0.3)3.0 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 3.3 (6)4.2 (1)3.6 (3)3.6 (3)3.3 (2)3.1 (2)4.6 (11)15/15
CGA-grid100 holtschulte noiseless 10 (18)70 (60)311 (289)1206 (1158)4466 (2973)2e50/15
CGA-grid16 holtschulte noiseless 5.1 (6)16 (5)71 (79)443 (915)1949 (4120)1.0e4 (6977)2e50/15
CGA-ring100 holtschulte noiseless 8.7 (12)35 (35)95 (65)251 (135)696 (679)1.0e4 (6279)2e50/15
CGA-ring16 holtschulte noiseless 4.8 (6)13 (7)33 (15)353 (518)680 (1783)2222 (1047)2e50/15
CMAES Hutter hutter noiseless 2.0 (0.8)3.2 (1)3.0 (0.5)12 (10)3030/15
DE Pal pal noiseless 3.3 (2)6.1 (2)7.5 (4)9.2 (2)10 (1)11 (1)13 (3)15/15
GA-100 holtschulte noiseless 10 (5)26 (9)77 (37)254 (352)1890 (2259)2e50/15
HCMA loshchilov noiseless 2.9 (2)5.8 (1)4.9 (10)4.8 (2)4.5 (4)4.3 (1)5.8 (0.6)15/15
HILL holtschulte noiseless 3.3 (5)21 (9)145 (37)370 (415)886 (1124)3122 (3941)2e50/15
HMLSL pal noiseless 1.5 (1.0)1.5 (0.7)1.3 (0.5)1.2 (0.7)1.2 (0.6)1.1 (0.4)1.2 (0.3)15/15
IP-10DDr liao noiseless 2.2 (1)3.0 (0.8)2.9 (1.0)3.1 (0.6)3.2 (0.5)3.0 (0.3)3.1 (0.3)15/15
IP-500 liao noiseless 2.2 (1)3.0 (1)2.9 (0.7)3.1 (0.8)3.2 (0.6)3.0 (0.3)3.1 (0.3)15/15
IPOP400D auger noiseless 2.0 (3)2.8 (1)3.1 (1)3.1 (0.8)3.1 (0.5)3.0 (0.3)3.2 (0.4)15/15
IP liao noiseless 2.2 (1)3.0 (1.0)2.9 (0.6)3.1 (1)3.2 (0.6)3.0 (0.5)3.1 (0.3)15/15
MEMPSODE voglis noiseless 2.0 (0.8)2.1 (0.9)1.7 (0.6)1.5 (0.5)1.5 (0.3)1.4 (0.3)1.5 (0.3)15/15
MLSL pal noiseless 1.5 (1.0)1.5 (0.9)1.3 (0.5)1.2 (0.6)1.2 (0.5)1.1 (0.2)1.2 (0.4)15/15
OQNLP pal noiseless 1.4 (0.5)1.7 (1)2.0 (0.5)2.0 (2)2.8 (2)3.6 (2)4.5 (1)12/15
P-DCN tran noiseless 8.8 (5)11 (9)9.1 (6)10 (5)23 (12)157 (213)212 (416)15/15
P-zero tran noiseless 11 (20)12 (17)11 (9)15 (9)36 (46)786 (79)6476 (6171)7/15
PRCGA sawyerr noiseless 7.3 (25)41 (136)51 (106)118 (102)155 (139)199 (147)220 (135)15/15
SMAC-BBOB hutter noiseless 1.1 (1)36 (70)3000/15
U-DCN tran noiseless 3.6 (6)14 (16)47 (27)175 (214)508 (923)7234 (1e4)7.6e4 (5e4)0/15
U-zero tran noiseless 3.4 (6)25 (41)138 (109)1458 (2534)3446 (3513)1.3e4 (1e4)3e60/15
fmincon pal noiseless 1.5 (1)1.5 (0.7)1.2 (0.5)1.2 (0.5)1.2 (0.3)1.1 (0.5)1.2 (0.4)15/15
fminunc pal noiseless 2.4 (3)3.3 (0.8)2.5 (0.8)2.2 (0.9)2.1 (0.9)2.1 (1)3.4 (4)15/15
lmm-CMA-ES auger noiseless 2.6 (2)3.2 (1)2.9 (0.8)3.3 (1)3.1 (2)3.3 (2)3.7 (0.8)15/15
simplex pal noiseless 5.8 (5)7.3 (4)4.8 (2)4.3 (2)3.7 (2)2.9 (1)2.6 (1)15/15
tany liao noiseless 1.8 (0.9)2.5 (0.7)3.0 (1)3.4 (0.7)3.5 (0.6)3.4 (0.3)3.5 (0.3)15/15
texp liao noiseless 1.8 (0.9)3.1 (2)3.1 (0.8)3.4 (1)3.8 (0.7)3.4 (0.3)3.5 (0.5)15/15

Δ fopt
f7, 3-D
1e1
11
1e0
65
1e-1
342
1e-2
464
1e-3
482
1e-5
482
1e-7
535
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.1 (2)2.1 (2)1.0 (0.6)0.99 (0.6)1.1 (0.9)1.1 (0.8)1.1 (0.8)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (3)1.9 (0.9)0.75 (0.4)0.95 (0.4)1.0 (0.3)1.0 (0.9)1.2 (0.8)15/15
CGA-grid100 holtschulte noiseless 5.8 (11)24 (15)76 (47)166 (252)375 (503)375 (545)884 (1029)4/15
CGA-grid16 holtschulte noiseless 6.4 (8)8.6 (6)54 (25)112 (168)225 (164)225 (239)209 (154)9/15
CGA-ring100 holtschulte noiseless 3.5 (4)14 (7)8.6 (10)32 (31)92 (107)92 (131)96 (12)13/15
CGA-ring16 holtschulte noiseless 5.2 (4)5.2 (2)8.2 (6)72 (27)111 (193)111 (213)104 (17)13/15
CMAES Hutter hutter noiseless 2.8 (2)1.6 (2)0.84 (0.5)0.87 (0.8)0.87 (0.6)0.87 (0.2)1.1 (0.6)1/15
DE Pal pal noiseless 4.2 (3)2.9 (2)1.3 (0.3)1.7 (1)2.0 (0.5)2.0 (0.6)2.1 (0.7)15/15
GA-100 holtschulte noiseless 4.9 (5)7.3 (6)8.6 (14)22 (87)61 (73)61 (133)63 (63)15/15
HCMA loshchilov noiseless 1.9 (1)2.0 (3)0.84 (0.5)1.0 (0.4)1.1 (0.9)1.1 (0.5)1.1 (0.8)15/15
HILL holtschulte noiseless 6.2 (2)9.4 (10)44 (32)173 (166)249 (299)249 (358)229 (189)9/15
HMLSL pal noiseless 3.9 (4)5.1 (2)2.4 (1)3.3 (1)3.9 (0.6)3.9 (2)3.8 (2)15/15
IP-10DDr liao noiseless 4.3 (3)4.0 (7)1.5 (1)1.2 (2)1.2 (0.8)1.2 (2)1.2 (1)15/15
IP-500 liao noiseless 4.3 (2)4.0 (2)1.5 (1)1.2 (2)1.2 (0.9)1.2 (2)1.2 (0.5)15/15
IPOP400D auger noiseless 1.8 (2)1.3 (0.4)0.99 (0.5)1.1 (0.7)1.2 (1)1.2 (0.9)1.1 (0.8)15/15
IP liao noiseless 4.3 (1)4.0 (8)1.5 (2)1.2 (2)1.2 (2)1.2 (0.8)1.2 (2)15/15
MEMPSODE voglis noiseless 6.5 (2)22 (20)12 (7)12 (6)13 (4)13 (6)13 (12)15/15
MLSL pal noiseless 4.9 (8)23 (17)174 (158)3e40/15
OQNLP pal noiseless 5.0 (2)4.2 (2)2.2 (0.8)4.3 (4)4.9 (2)4.9 (3)5.7 (3)5/15
P-DCN tran noiseless 41 (7)648 (43)151 (425)112 (605)111 (326)111 (583)100 (57)15/15
P-zero tran noiseless 15 (46)123 (174)101 (72)76 (68)74 (53)74 (69)66 (31)15/15
PRCGA sawyerr noiseless 2.7 (5)7.2 (33)7.3 (11)7.8 (8)20 (36)20 (9)18 (32)14/15
SMAC-BBOB hutter noiseless 1.2 (1)0.92 (0.6)0.81 (1)3000/15
U-DCN tran noiseless 7.1 (3)18 (16)312 (308)1071 (2011)4021 (4679)4021 (3779)3624 (7273)10/15
U-zero tran noiseless 4.6 (5)29 (92)278 (931)455 (394)621 (750)621 (934)566 (451)15/15
fmincon pal noiseless 5.2 (4)22 (25)125 (172)951 (747)3e40/15
fminunc pal noiseless 4.2 (5)25 (24)140 (137)3e40/15
lmm-CMA-ES auger noiseless 1.5 (0.9)2.2 (4)1.1 (1)1.0 (0.8)1.1 (0.9)1.1 (2)1.0 (1)15/15
simplex pal noiseless 3.0 (3)8.0 (7)20 (18)103 (150)277 (187)277 (362)249 (455)3/15
tany liao noiseless 3.3 (3)1.6 (0.7)0.84 (0.8)1.1 (2)1.1 (0.5)1.1 (0.2)1.0 (0.9)15/15
texp liao noiseless 2.3 (1)5.0 (9)2.1 (2)2.1 (1)2.2 (0.7)2.2 (1)2.1 (2)15/15

Δ fopt
f8, 3-D
1e1
27
1e0
45
1e-1
152
1e-2
179
1e-3
188
1e-5
198
1e-7
208
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.7 (0.8)8.2 (4)4.0 (1)4.1 (2)4.3 (2)4.6 (1)4.8 (1.0)15/15
BIPOP-saACM-k loshchilov noiseless 2.9 (1)4.5 (2)2.0 (0.6)2.0 (0.6)2.1 (0.5)2.1 (0.6)2.2 (0.9)15/15
CGA-grid100 holtschulte noiseless 32 (28)129 (45)1716 (1811)6111 (6002)2e50/15
CGA-grid16 holtschulte noiseless 11 (9)299 (937)4079 (3871)5803 (2723)2e50/15
CGA-ring100 holtschulte noiseless 24 (20)62 (37)105 (71)420 (34)1511 (2056)2e50/15
CGA-ring16 holtschulte noiseless 9.3 (5)34 (22)785 (986)2326 (3978)3316 (3790)2e50/15
CMAES Hutter hutter noiseless 3.7 (2)10 (13)30 (34)3030/15
DE Pal pal noiseless 6.7 (3)14 (17)9.4 (5)11 (4)13 (3)17 (4)20 (4)15/15
GA-100 holtschulte noiseless 14 (11)48 (24)237 (279)2587 (4621)1.1e4 (2e4)2e50/15
HCMA loshchilov noiseless 2.5 (4)6.6 (3)2.6 (0.7)2.5 (1)2.5 (1)2.6 (1)2.6 (1)15/15
HILL holtschulte noiseless 4.0 (2)552 (22)1661 (2222)5550 (5032)2e50/15
HMLSL pal noiseless 1.1 (0.5)1.5 (2)0.63 (0.7)0.62 (0.4)0.64 (0.3)0.68 (0.4)0.68 (0.5)15/15
IP-10DDr liao noiseless 3.0 (0.9)8.6 (11)5.0 (4)5.1 (2)5.4 (0.7)5.8 (2)6.0 (3)15/15
IP-500 liao noiseless 3.0 (2)8.6 (10)5.0 (1)5.1 (2)5.4 (3)5.8 (3)6.0 (2)15/15
IPOP400D auger noiseless 2.7 (1)7.3 (6)4.2 (2)4.5 (0.9)4.7 (2)5.0 (0.8)5.4 (0.8)15/15
IP liao noiseless 3.0 (0.8)8.6 (10)5.0 (2)5.1 (2)5.4 (3)5.8 (3)6.0 (1)15/15
MEMPSODE voglis noiseless 3.0 (0.3)2.9 (2)1.1 (0.6)1.1 (0.3)1.1 (0.5)1.2 (0.4)1.3 (0.5)15/15
MLSL pal noiseless 1.1 (0.3)1.5 (1)0.63 (0.7)0.62 (0.6)0.64 (0.4)0.68 (0.4)0.68 (0.3)15/15
OQNLP pal noiseless 1.1 (0.7)1.5 (0.6)0.68 (0.4)0.72 (0.3)0.75 (0.3)0.78 (0.2)2.9 (4)11/15
P-DCN tran noiseless 12 (10)167 (535)198 (236)341 (237)989 (889)4245 (2462)1.4e4 (2e4)3/15
P-zero tran noiseless 49 (159)583 (1219)520 (391)1520 (635)2270 (892)7.6e4 (1e5)3e60/15
PRCGA sawyerr noiseless 4.1 (2)42 (5)258 (198)568 (505)1267 (1257)3126 (2394)6374 (1e4)1/15
SMAC-BBOB hutter noiseless 3.3 (2)10 (13)9.3 (8)3000/15
U-DCN tran noiseless 9.2 (8)284 (877)2664 (2983)5.1e4 (5e4)1.0e5 (1e5)3e60/15
U-zero tran noiseless 7.7 (5)79 (432)5.9e4 (6e4)2.3e5 (2e5)3e60/15
fmincon pal noiseless 1.1 (0.4)1.5 (1)0.63 (0.5)0.62 (0.4)0.65 (0.4)0.69 (0.5)0.68 (0.3)15/15
fminunc pal noiseless 1.00 (0.9)1.5 (1)0.73 (0.4)0.73 (0.2)0.76 (0.2)0.76 (0.2)0.76 (0.2)15/15
lmm-CMA-ES auger noiseless 1.7 (1)2.1 (1)1.1 (0.2)1.2 (0.4)1.2 (0.1)1.3 (0.3)1.3 (0.1)15/15
simplex pal noiseless 4.5 (4)4.7 (3)1.8 (0.8)1.9 (0.6)1.9 (0.6)2.0 (0.7)2.0 (0.3)15/15
tany liao noiseless 2.3 (1)7.0 (6)4.7 (2)5.0 (1)5.3 (1)5.6 (1.0)5.9 (1)15/15
texp liao noiseless 2.7 (1)7.0 (8)4.7 (4)5.0 (1)5.3 (2)5.6 (2)5.7 (2)15/15

Δ fopt
f9, 3-D
1e1
21
1e0
65
1e-1
127
1e-2
149
1e-3
159
1e-5
169
1e-7
178
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.4 (2)7.4 (6)5.9 (5)5.9 (3)5.9 (4)6.2 (2)6.3 (4)15/15
BIPOP-saACM-k loshchilov noiseless 2.9 (1)2.6 (1)2.4 (0.9)2.4 (1)2.4 (0.4)2.5 (0.9)2.5 (0.5)15/15
CGA-grid100 holtschulte noiseless 30 (16)258 (26)1526 (2344)7212 (9826)1.4e4 (9434)2e50/15
CGA-grid16 holtschulte noiseless 17 (11)554 (656)2465 (2374)1.5e4 (1e4)2e50/15
CGA-ring100 holtschulte noiseless 30 (27)47 (29)200 (332)860 (1304)1920 (1831)1.3e4 (2e4)2e50/15
CGA-ring16 holtschulte noiseless 13 (9)59 (66)1585 (1776)1.4e4 (9312)2e50/15
CMAES Hutter hutter noiseless 3.4 (0.7)6.7 (7)3030/15
DE Pal pal noiseless 8.5 (5)10 (7)11 (6)12 (6)14 (6)18 (4)22 (4)15/15
GA-100 holtschulte noiseless 16 (15)39 (23)392 (612)2284 (3272)1.3e4 (3e4)2e50/15
HCMA loshchilov noiseless 2.7 (3)4.2 (2)3.1 (2)3.0 (0.9)3.0 (0.9)3.0 (0.9)3.0 (1)15/15
HILL holtschulte noiseless 7.1 (8)426 (612)2607 (3701)1.4e4 (2e4)1.4e4 (1e4)2e50/15
HMLSL pal noiseless 0.52 (0)0.45 (0)0.41 (0)0.48 (0)0.50 (3e-3)0.52 (0.0)0.54 (1e-3)15/15
IP-10DDr liao noiseless 4.2 (2)6.9 (5)6.3 (6)6.6 (2)6.8 (2)7.0 (3)7.2 (2)15/15
IP-500 liao noiseless 4.2 (3)6.9 (8)6.3 (2)6.6 (4)6.8 (2)7.0 (2)7.2 (2)15/15
IPOP400D auger noiseless 2.6 (1)3.6 (2)3.8 (2)4.4 (2)4.6 (1)4.9 (1)5.3 (2)15/15
IP liao noiseless 4.2 (3)6.9 (5)6.3 (3)6.6 (4)6.8 (2)7.0 (3)7.2 (4)15/15
MEMPSODE voglis noiseless 3.7 (0.5)2.4 (1)1.6 (1)1.6 (0.6)1.6 (0.8)1.7 (0.5)1.7 (0.8)15/15
MLSL pal noiseless 0.52 (0)0.45 (0)0.41 (0)0.48 (5e-3)0.50 (2e-3)0.52 (7e-3)0.54 (1e-3)15/15
OQNLP pal noiseless 0.48 (0)0.21 (0.0)0.38 (1e-2)0.48 (0.0)0.53 (0.0)0.58 (0.0)0.60 (0.0)15/15
P-DCN tran noiseless 13 (19)459 (175)318 (796)550 (546)1181 (816)5377 (4022)1.9e4 (3e4)6/15
P-zero tran noiseless 13 (11)1312 (3382)911 (1570)1281 (1568)2946 (3572)4.7e4 (4e4)2.5e5 (5e5)0/15
PRCGA sawyerr noiseless 4.8 (2)23 (39)393 (413)1097 (1143)2406 (3996)1.8e4 (4e4)2e50/15
SMAC-BBOB hutter noiseless 6.9 (3)69 (74)3000/15
U-DCN tran noiseless 14 (6)255 (702)3798 (1e4)2.4e4 (2e4)4.8e4 (5e4)3e60/15
U-zero tran noiseless 10 (14)903 (1789)2.0e4 (4e4)3.0e5 (3e5)3e60/15
fmincon pal noiseless 0.52 (0)0.45 (0)0.41 (0)0.48 (5e-3)0.50 (2e-3)0.52 (0)0.54 (0)15/15
fminunc pal noiseless 0.43 (0)0.14 (0)★40.38 (0.0)0.45 (0.0)0.48 (0.0)0.51 (0.0)0.51 (0.0)15/15
lmm-CMA-ES auger noiseless 1.6 (0.5)1.6 (0.8)1.4 (0.5)1.5 (0.3)1.5 (0.2)1.6 (0.2)1.6 (0.2)15/15
simplex pal noiseless 1.3 (0.1)1.1 (0.4)1.5 (0.2)1.5 (0.3)1.5 (0.3)1.5 (0.3)1.6 (0.2)15/15
tany liao noiseless 3.0 (1)5.6 (6)5.6 (2)6.1 (2)6.2 (2)6.5 (3)6.8 (2)15/15
texp liao noiseless 1.9 (1)5.0 (7)5.8 (3)6.4 (3)6.5 (3)6.8 (3)7.0 (2)15/15

Δ fopt
f10, 3-D
1e1
114
1e0
152
1e-1
168
1e-2
180
1e-3
194
1e-5
218
1e-7
242
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.6 (0.9)3.8 (1.0)3.7 (0.8)3.8 (0.4)3.7 (0.6)3.7 (0.6)3.7 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 1.5 (0.3)1.3 (0.2)1.3 (0.1)1.3 (0.2)1.3 (0.1)1.3 (0.2)1.3 (0.2)15/15
CGA-grid100 holtschulte noiseless 1260 (2692)1.4e4 (2e4)2e50/15
CGA-grid16 holtschulte noiseless 1584 (2032)2e50/15
CGA-ring100 holtschulte noiseless 166 (132)3265 (3834)2e50/15
CGA-ring16 holtschulte noiseless 612 (787)3090 (3090)2e50/15
CMAES Hutter hutter noiseless 9.3 (9)3030/15
DE Pal pal noiseless 9.2 (3)10 (4)12 (5)14 (4)16 (4)19 (4)21 (6)15/15
GA-100 holtschulte noiseless 1284 (1480)4168 (9427)1.3e4 (8705)2e50/15
HCMA loshchilov noiseless 1.9 (0.3)1.7 (0.2)1.6 (0.2)1.6 (0.2)1.6 (0.2)1.5 (0.1)1.5 (0.2)15/15
HILL holtschulte noiseless 1382 (1960)6692 (6699)2e50/15
HMLSL pal noiseless 0.45 (0.3)0.39 (0.1)0.40 (0.1)0.41 (0.2)0.83 (0.2)10 (21)40 (64)15/15
IP-10DDr liao noiseless 5.3 (3)5.8 (2)5.8 (0.5)5.7 (0.7)5.6 (0.3)5.4 (0.5)5.3 (0.4)15/15
IP-500 liao noiseless 5.3 (3)5.8 (2)5.8 (0.5)5.7 (0.7)5.6 (0.6)5.4 (0.5)5.3 (0.6)15/15
IPOP400D auger noiseless 4.4 (2)4.1 (0.7)4.3 (0.6)4.3 (0.4)4.3 (0.6)4.3 (0.3)4.2 (0.3)15/15
IP liao noiseless 5.3 (2)5.8 (2)5.8 (1.0)5.7 (0.5)5.6 (0.6)5.4 (0.5)5.3 (0.4)15/15
MEMPSODE voglis noiseless 1.8 (0.8)1.6 (0.5)1.5 (0.5)1.5 (0.7)1.5 (0.6)1.4 (0.4)1.4 (0.5)15/15
MLSL pal noiseless 0.45 (0.3)0.39 (0.2)0.40 (0.2)0.41 (0.2)0.91 (2)5.1 (5)76 (110)10/15
OQNLP pal noiseless 0.45 (0.1)0.45 (0.1)0.68 (0.4)2.3 (3)3.9 (4)17 (13)122 (52)1/15
P-DCN tran noiseless 697 (315)2190 (703)4292 (3563)9830 (1e4)1.8e4 (3e4)9.7e4 (1e5)1.8e5 (1e5)0/15
P-zero tran noiseless 1573 (6355)1.0e4 (2e4)2.8e4 (4e4)5.0e4 (4e4)6.8e4 (9e4)2.0e5 (5e5)3e60/15
PRCGA sawyerr noiseless 557 (241)1989 (2000)2935 (6806)8283 (1e4)1.6e4 (3e4)2e50/15
SMAC-BBOB hutter noiseless 3000/15
U-DCN tran noiseless 1360 (3687)1.3e4 (1e4)1.2e5 (2e5)3e60/15
U-zero tran noiseless 1.2e4 (1e4)2.8e4 (4e4)3e60/15
fmincon pal noiseless 0.45 (0.3)0.39 (0.1)0.40 (0.2)0.41 (0.2)0.45 (0.1)9.1 (27)95 (124)10/15
fminunc pal noiseless 0.72 (0.2)0.95 (0.4)1.2 (0.6)1.2 (0.5)1.5 (1)6.7 (9)83 (262)5/15
lmm-CMA-ES auger noiseless 1.0 (0.5)1.1 (0.2)1.1 (0.2)1.1 (0.3)1.1 (0.2)1.1 (0.1)1.0 (0.1)15/15
simplex pal noiseless 2.9 (2)2.7 (1)2.8 (0.8)2.9 (0.6)2.7 (0.7)2.5 (0.2)2.4 (0.4)15/15
tany liao noiseless 4.7 (3)5.5 (2)5.8 (0.3)5.7 (0.5)5.5 (0.4)5.3 (0.5)5.2 (0.4)15/15
texp liao noiseless 3.5 (1)4.4 (2)4.8 (1)5.0 (1)4.9 (0.5)4.8 (0.5)4.7 (0.4)15/15

Δ fopt
f11, 3-D
1e1
67
1e0
105
1e-1
227
1e-2
263
1e-3
277
1e-5
302
1e-7
327
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 6.7 (3)5.3 (2)2.7 (0.5)2.6 (0.5)2.6 (0.3)2.7 (0.4)2.8 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (0.5)2.0 (0.4)0.97 (0.1)0.90 (0.1)0.91 (0.1)0.94 (0.1)0.97 (0.1)15/15
CGA-grid100 holtschulte noiseless 695 (4480)3367 (6299)9905 (8095)2e50/15
CGA-grid16 holtschulte noiseless 275 (149)1072 (728)4865 (3026)2e50/15
CGA-ring100 holtschulte noiseless 72 (69)589 (512)1509 (1952)2e50/15
CGA-ring16 holtschulte noiseless 54 (106)927 (1129)2839 (3320)8153 (5846)2e50/15
CMAES Hutter hutter noiseless 65 (90)3030/15
DE Pal pal noiseless 9.3 (5)11 (3)8.3 (2)8.8 (2)10 (2)13 (2)15 (0.7)15/15
GA-100 holtschulte noiseless 652 (1776)2597 (2842)9360 (6443)2e50/15
HCMA loshchilov noiseless 2.6 (1)2.3 (0.3)1.1 (0.2)1.0 (0.1)1.0 (0.1)1.0 (0.1)1.1 (0.1)15/15
HILL holtschulte noiseless 197 (143)503 (334)2e50/15
HMLSL pal noiseless 0.35 (0.1)0.27 (0.1)0.15 (0.0)0.15 (0.0)0.60 (0.7)10 (27)49 (35)15/15
IP-10DDr liao noiseless 10 (5)8.4 (2)4.5 (1)4.1 (0.5)4.1 (0.7)4.1 (0.8)4.1 (0.6)15/15
IP-500 liao noiseless 10 (5)8.4 (3)4.5 (0.8)4.1 (0.7)4.1 (0.8)4.1 (0.7)4.1 (0.6)15/15
IPOP400D auger noiseless 8.4 (4)7.4 (1)3.8 (0.7)3.5 (0.5)3.5 (0.4)3.5 (0.3)3.5 (0.3)15/15
IP liao noiseless 10 (6)8.4 (2)4.5 (1)4.1 (0.7)4.1 (0.7)4.1 (0.8)4.1 (0.5)15/15
MEMPSODE voglis noiseless 3.0 (1)2.7 (0.4)1.4 (0.3)1.3 (0.2)1.2 (0.2)1.2 (0.1)1.2 (0.2)15/15
MLSL pal noiseless 0.35 (0.1)0.27 (0.1)0.15 (0.1)0.15 (0.0)2.1 (7)9.2 (17)201 (280)2/15
OQNLP pal noiseless 0.73 (0.3)0.52 (0.1)0.37 (0.5)1.6 (1)5.5 (5)36 (94)1e40/15
P-DCN tran noiseless 138 (201)481 (250)333 (173)414 (163)756 (385)8308 (1e4)3e60/15
P-zero tran noiseless 528 (844)1095 (851)720 (432)773 (234)1530 (2219)3.5e4 (4e4)3e60/15
PRCGA sawyerr noiseless 155 (136)965 (2612)4750 (8415)4169 (4945)2e50/15
SMAC-BBOB hutter noiseless 5.7 (4)41 (37)3000/15
U-DCN tran noiseless 143 (642)769 (747)1.2e4 (1e4)3e60/15
U-zero tran noiseless 194 (130)1909 (1888)7122 (8062)5.0e4 (4e4)1.6e5 (2e5)3e60/15
fmincon pal noiseless 0.35 (0.1)0.27 (0.1)0.15 (0.1)0.15 (0.0)1.4 (0.1)37 (67)179 (193)1/15
fminunc pal noiseless 0.85 (0.5)0.92 (0.3)0.79 (0.1)1.6 (1)4.6 (6)55 (117)406 (634)1/15
lmm-CMA-ES auger noiseless 1.4 (0.7)1.6 (0.4)0.88 (0.1)0.80 (0.1)0.79 (0.2)0.79 (0.2)0.79 (0.1)15/15
simplex pal noiseless 4.8 (4)5.4 (3)2.7 (0.7)2.5 (0.4)2.4 (0.5)2.3 (0.8)2.2 (0.6)15/15
tany liao noiseless 10 (4)8.0 (3)4.2 (0.8)3.9 (0.6)3.9 (0.4)3.9 (0.5)3.9 (0.3)15/15
texp liao noiseless 8.7 (5)7.9 (3)4.0 (0.6)3.6 (0.5)3.6 (0.5)3.6 (0.4)3.6 (0.5)15/15

Δ fopt
f12, 3-D
1e1
65
1e0
168
1e-1
338
1e-2
401
1e-3
445
1e-5
696
1e-7
790
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 12 (14)8.4 (12)5.7 (8)5.6 (7)5.5 (9)4.2 (3)4.8 (5)15/15
BIPOP-saACM-k loshchilov noiseless 3.2 (3)3.6 (5)2.9 (5)3.0 (4)4.3 (16)6.1 (12)12 (23)15/15
CGA-grid100 holtschulte noiseless 983 (797)2845 (2122)2e50/15
CGA-grid16 holtschulte noiseless 1781 (1894)5953 (1e4)2e50/15
CGA-ring100 holtschulte noiseless 336 (271)711 (526)919 (685)2e50/15
CGA-ring16 holtschulte noiseless 727 (1228)1979 (2289)3061 (4438)2e50/15
CMAES Hutter hutter noiseless 6.5 (9)27 (15)3030/15
DE Pal pal noiseless 27 (23)27 (28)21 (18)21 (12)21 (13)17 (9)17 (10)15/15
GA-100 holtschulte noiseless 1015 (1823)3749 (3116)6389 (7101)2e50/15
HCMA loshchilov noiseless 3.9 (2)4.6 (10)2.8 (9)2.6 (1)3.2 (2)4.1 (6)14 (20)15/15
HILL holtschulte noiseless 2086 (2299)2497 (3147)6487 (6435)2e50/15
HMLSL pal noiseless 0.89 (0.2)0.77 (0.6)0.66 (0.6)0.67 (0.4)0.68 (0.6)4.9 (16)16 (37)14/15
IP-10DDr liao noiseless 8.0 (11)6.8 (6)4.8 (3)4.9 (3)5.0 (3)4.2 (3)4.3 (3)15/15
IP-500 liao noiseless 8.0 (6)6.8 (2)4.8 (5)4.9 (3)5.0 (3)4.2 (3)4.3 (3)15/15
IPOP400D auger noiseless 5.9 (6)7.0 (4)4.4 (5)4.9 (3)5.2 (6)3.5 (4)3.3 (2)8/15
IP liao noiseless 8.0 (6)6.8 (7)4.8 (4)4.9 (4)5.0 (3)4.2 (3)4.3 (2)15/15
MEMPSODE voglis noiseless 3.5 (2)2.6 (2)1.8 (2)1.6 (1)1.6 (1)1.2 (1)1.6 (0.9)15/15
MLSL pal noiseless 0.89 (0.2)0.77 (0.5)0.66 (0.4)0.67 (0.6)0.68 (0.4)3.2 (6)31 (33)6/15
OQNLP pal noiseless 1.3 (1)1.4 (1)11 (16)10 (25)12 (8)42 (30)106 (133)0/15
P-DCN tran noiseless 1.8e4 (2e4)1.6e4 (3e4)2.0e4 (3e4)5.0e4 (1e5)9.5e4 (8e4)3e60/15
P-zero tran noiseless 2.6e4 (4e4)4.9e4 (8e4)5.8e4 (4e4)1.0e5 (2e5)3e60/15
PRCGA sawyerr noiseless 86 (90)213 (73)245 (576)364 (401)686 (883)9e40/15
SMAC-BBOB hutter noiseless 22 (74)3000/15
U-DCN tran noiseless 1.2e4 (4e4)2.7e4 (2e4)5.8e4 (9e4)1.1e5 (9e4)3e60/15
U-zero tran noiseless 1.4e4 (2e4)3.6e4 (1e5)3.6e4 (6e4)5.0e4 (5e4)9.9e4 (1e5)3e60/15
fmincon pal noiseless 0.88 (0.9)0.77 (0.5)0.65 (0.6)0.66 (0.4)0.68 (0.5)1.8 (1)10 (14)8/15
fminunc pal noiseless 0.93 (0.4)0.80 (0.8)0.64 (0.6)0.63 (0.5)0.67 (0.5)1.4 (1)32 (53)5/15
lmm-CMA-ES auger noiseless 2.3 (4)1.6 (2)1.4 (0.8)1.4 (0.4)1.4 (2)1.2 (1)1.2 (0.6)13/15
simplex pal noiseless 3.8 (2)2.9 (1)1.9 (0.9)1.8 (1)1.8 (1)1.4 (1)1.4 (0.6)15/15
tany liao noiseless 7.5 (5)7.4 (7)5.4 (3)5.5 (5)5.5 (4)4.5 (2)4.6 (2)15/15
texp liao noiseless 10 (9)10 (11)7.2 (4)6.9 (6)6.8 (6)5.3 (4)5.2 (4)15/15

Δ fopt
f13, 3-D
1e1
49
1e0
85
1e-1
108
1e-2
136
1e-3
215
1e-5
281
1e-7
365
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.2 (3)4.0 (2)4.2 (1)4.2 (0.7)3.1 (0.5)3.4 (0.4)3.4 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (0.8)1.6 (0.4)1.7 (0.3)1.7 (0.3)1.3 (0.4)1.3 (0.3)1.2 (0.3)15/15
CGA-grid100 holtschulte noiseless 602 (440)4373 (4659)2e50/15
CGA-grid16 holtschulte noiseless 245 (530)5043 (2984)9717 (9466)2e50/15
CGA-ring100 holtschulte noiseless 58 (30)393 (1370)2849 (2021)1.6e4 (4e4)2e50/15
CGA-ring16 holtschulte noiseless 44 (79)2154 (1392)6349 (7930)2e50/15
CMAES Hutter hutter noiseless 4.0 (0.2)10 (8)3030/15
DE Pal pal noiseless 6.1 (1)9.0 (3)15 (2)17 (2)16 (2)18 (2)19 (4)15/15
GA-100 holtschulte noiseless 45 (27)1021 (957)4632 (5092)2e50/15
HCMA loshchilov noiseless 2.4 (1)2.2 (1)2.5 (0.5)2.2 (0.3)1.6 (0.3)1.5 (0.3)1.4 (0.2)15/15
HILL holtschulte noiseless 421 (885)2218 (3088)9774 (1e4)2e50/15
HMLSL pal noiseless 0.90 (0.2)0.70 (0.1)0.75 (0.1)0.75 (0.1)0.76 (0.1)26 (19)45 (5)15/15
IP-10DDr liao noiseless 3.8 (1)6.6 (4)7.3 (2)6.9 (1)5.0 (1)5.5 (1)5.2 (0.5)15/15
IP-500 liao noiseless 3.8 (3)6.6 (4)7.3 (2)6.9 (2)5.0 (1)5.5 (0.9)5.2 (0.4)15/15
IPOP400D auger noiseless 4.1 (3)4.7 (2)5.0 (2)5.7 (1)4.6 (1)4.4 (0.5)4.3 (0.7)12/15
IP liao noiseless 3.8 (3)6.6 (3)7.3 (3)6.9 (1)5.0 (0.7)5.5 (0.8)5.2 (0.6)15/15
MEMPSODE voglis noiseless 2.9 (0.9)2.1 (0.8)2.4 (0.6)2.1 (0.7)1.5 (0.4)1.5 (1.0)1.5 (0.9)15/15
MLSL pal noiseless 0.90 (0.1)0.70 (0.1)0.75 (0.1)0.75 (0.1)0.84 (0.0)114 (100)4e40/15
OQNLP pal noiseless 1.3 (0.4)1.0 (0.3)0.96 (0.4)1.3 (2)7.2 (5)435 (1059)92100/15
P-DCN tran noiseless 149 (408)1372 (3087)1.8e4 (2e4)4.0e4 (2e4)6.3e4 (1e5)1.6e5 (2e5)3e60/15
P-zero tran noiseless 3394 (1598)8682 (8056)5.2e4 (4e4)1.5e5 (4e5)3e60/15
PRCGA sawyerr noiseless 9.5 (2)408 (315)641 (287)1469 (1257)1678 (3568)3701 (3059)5758 (4986)1/15
SMAC-BBOB hutter noiseless 1.6 (0.6)8.7 (7)3000/15
U-DCN tran noiseless 4170 (8761)3.1e4 (9e4)6.5e4 (8e4)3e60/15
U-zero tran noiseless 701 (471)4.9e4 (5e4)1.3e5 (2e5)3e60/15
fmincon pal noiseless 0.90 (0.1)0.70 (0.1)0.75 (0.1)0.75 (0.1)0.79 (0.1)156 (138)3e40/15
fminunc pal noiseless 1.0 (0.4)1.0 (0.3)1.1 (0.2)1.0 (0.1)1.5 (2)1917 (1350)4e40/15
lmm-CMA-ES auger noiseless 1.4 (0.3)1.8 (0.9)1.8 (0.5)1.8 (0.3)1.3 (0.2)1.3 (0.3)1.3 (0.2)15/15
simplex pal noiseless 6.5 (7)7.1 (3)6.8 (2)5.9 (2)3.9 (1)3.3 (2)2.7 (0.5)15/15
tany liao noiseless 3.4 (2)5.3 (3)5.9 (3)6.9 (0.9)5.1 (1)5.2 (0.7)4.9 (1.0)15/15
texp liao noiseless 3.4 (1)5.5 (4)6.5 (2)6.4 (0.8)4.8 (1.0)4.9 (0.6)4.8 (0.4)15/15

Δ fopt
f14, 3-D
1e1
2.0
1e0
17
1e-1
28
1e-2
43
1e-3
71
1e-5
110
1e-7
194
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.1 (3)3.5 (2)4.1 (2)4.1 (1)4.0 (1)5.1 (0.8)4.1 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 3.2 (4)2.7 (1)3.1 (1)3.3 (0.9)2.7 (0.6)2.5 (0.4)1.9 (0.1)15/15
CGA-grid100 holtschulte noiseless 2.6 (2)18 (11)58 (27)277 (567)3553 (3581)2e50/15
CGA-grid16 holtschulte noiseless 2.6 (3)8.3 (7)16 (7)192 (257)4137 (3046)2e50/15
CGA-ring100 holtschulte noiseless 3.5 (3)9.2 (9)54 (41)105 (54)560 (1470)2e50/15
CGA-ring16 holtschulte noiseless 2.0 (2)7.6 (5)16 (6)76 (36)2382 (1992)2e50/15
CMAES Hutter hutter noiseless 3.5 (4)2.6 (4)3.8 (0.8)3.7 (1)4.9 (2)3030/15
DE Pal pal noiseless 1.5 (0.8)3.5 (2)7.7 (2)8.6 (2)10 (2)16 (5)17 (3)15/15
GA-100 holtschulte noiseless 2.2 (2)7.5 (7)28 (8)68 (28)387 (259)9391 (8070)2e50/15
HCMA loshchilov noiseless 4.7 (4)1.9 (0.4)3.5 (3)4.4 (1)3.5 (0.3)3.1 (0.8)2.3 (0.3)15/15
HILL holtschulte noiseless 5.1 (6)2.8 (2)5.9 (3)93 (45)3732 (4360)2e50/15
HMLSL pal noiseless 1.5 (2)0.73 (0.4)0.79 (0.3)0.83 (0.2)0.69 (0.1)0.86 (0.2)36 (17)15/15
IP-10DDr liao noiseless 2.6 (2)2.7 (2)3.7 (0.9)4.4 (1)5.3 (2)8.0 (1.0)7.0 (0.9)15/15
IP-500 liao noiseless 2.6 (2)2.7 (1)3.7 (2)4.4 (2)5.3 (1)8.0 (0.9)7.0 (1)15/15
IPOP400D auger noiseless 1.8 (0.8)2.1 (1)3.6 (1)4.3 (1)4.7 (1)6.3 (2)5.8 (0.6)15/15
IP liao noiseless 2.6 (2)2.7 (2)3.7 (1)4.4 (2)5.3 (2)8.0 (1)7.0 (0.9)15/15
MEMPSODE voglis noiseless 3.9 (2)3.4 (2)3.4 (0.5)2.8 (0.5)2.0 (0.3)1.8 (0.2)1.3 (0.1)15/15
MLSL pal noiseless 1.5 (2)0.73 (0.2)0.79 (0.4)0.83 (0.2)0.69 (0.2)0.86 (0.2)1073 (2588)0/15
OQNLP pal noiseless 3.0 (4)1.4 (0.5)1.3 (0.5)1.2 (0.4)0.98 (0.3)5.3 (8)104 (87)0/15
P-DCN tran noiseless 1.8 (2)10 (7)11 (5)10 (5)22 (16)4819 (2445)2.2e5 (3e5)0/15
P-zero tran noiseless 1.7 (0.6)8.2 (7)9.1 (7)10 (6)42 (21)1.9e4 (3e4)3e60/15
PRCGA sawyerr noiseless 2.2 (1)5.0 (7)9.2 (9)40 (6)99 (100)1197 (1156)1.2e4 (1e4)0/15
SMAC-BBOB hutter noiseless 1.1 (0.9)1.9 (1)4.2 (1)9.2 (5)3000/15
U-DCN tran noiseless 2.1 (4)3.9 (4)14 (7)68 (66)890 (1168)3e60/15
U-zero tran noiseless 1.7 (2)3.3 (2)12 (12)112 (178)1.9e4 (2e4)3.9e5 (3e5)3e60/15
fmincon pal noiseless 1.5 (1)0.73 (0.1)0.79 (0.2)0.83 (0.1)0.69 (0.2)0.86 (0.2)662 (1310)0/15
fminunc pal noiseless 1.7 (2)0.92 (0.6)1.0 (0.6)1.0 (0.5)0.87 (0.4)0.89 (0.3)165 (135)0/15
lmm-CMA-ES auger noiseless 1.9 (2)1.7 (0.5)1.6 (0.5)1.7 (0.5)1.8 (0.4)2.1 (0.4)1.7 (0.2)15/15
simplex pal noiseless 9.4 (16)7.3 (3)6.8 (3)5.2 (1)3.5 (0.7)2.8 (0.2)1.9 (0.2)15/15
tany liao noiseless 3.0 (4)2.2 (2)3.4 (0.6)3.7 (0.7)5.0 (1)7.2 (0.7)6.8 (0.3)15/15
texp liao noiseless 3.1 (0.8)2.2 (1)2.9 (2)3.8 (2)4.9 (3)6.9 (2)6.1 (0.8)15/15

Δ fopt
f15, 3-D
1e1
121
1e0
1372
1e-1
6285
1e-2
8282
1e-3
8429
1e-5
8787
1e-7
9041
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.2 (0.5)1.6 (2)1.6 (1)1.2 (0.7)1.2 (1)1.2 (1)1.2 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 1.5 (0.6)1.8 (2)0.80 (0.5)0.62 (0.6)0.62 (0.5)0.61 (0.4)0.60 (0.6)15/15
CGA-grid100 holtschulte noiseless 10 (9)118 (113)2e50/15
CGA-grid16 holtschulte noiseless 4.0 (4)92 (197)71 (93)57 (35)78 (120)2e50/15
CGA-ring100 holtschulte noiseless 7.1 (1)42 (56)44 (44)48 (15)128 (167)2e50/15
CGA-ring16 holtschulte noiseless 3.4 (2)61 (89)68 (73)53 (73)56 (101)2e50/15
CMAES Hutter hutter noiseless 1.2 (1)3030/15
DE Pal pal noiseless 1.7 (0.6)2.7 (1)2.2 (5)1.7 (0.1)1.8 (4)1.7 (0.2)1.7 (2)13/15
GA-100 holtschulte noiseless 5.4 (4)62 (101)32 (83)26 (47)40 (42)2e50/15
HCMA loshchilov noiseless 1.8 (0.9)1.2 (1)0.76 (0.4)0.59 (0.6)0.59 (0.2)0.58 (0.3)0.57 (0.7)15/15
HILL holtschulte noiseless 3.2 (3)144 (206)338 (257)258 (362)257 (262)2e50/15
HMLSL pal noiseless 2.9 (1)1.4 (2)2.4 (3)1.8 (8)1.8 (4)1.7 (4)1.7 (4)13/15
IP-10DDr liao noiseless 1.6 (0.6)2.6 (3)1.9 (3)1.4 (1)1.4 (2)1.4 (1)1.4 (2)15/15
IP-500 liao noiseless 1.6 (3)2.6 (2)1.5 (1)1.2 (1)1.2 (1)1.2 (0.8)1.2 (0.8)15/15
IPOP400D auger noiseless 0.91 (0.5)1.5 (2)2.2 (2)1.7 (0.9)1.7 (2)1.6 (2)1.6 (2)1/15
IP liao noiseless 1.6 (0.5)2.6 (3)1.5 (1)1.2 (0.2)1.2 (0.7)1.2 (1)1.2 (1)15/15
MEMPSODE voglis noiseless 7.9 (9)5.4 (3)4.2 (3)3.2 (3)3.1 (3)3.0 (1)2.9 (1)15/15
MLSL pal noiseless 2.5 (1)4.9 (7)6.2 (3)4.7 (6)4.6 (4)4.4 (7)4.3 (5)8/15
OQNLP pal noiseless 3.0 (0.1)1.5 (3)0.71 (0.6)0.54 (0.3)0.53 (0.4)0.51 (0.7)0.53 (0.3)10/15
P-DCN tran noiseless 2739 (531)1449 (1387)6701 (1e4)5086 (1e4)4997 (1e4)4794 (2646)4660 (5226)1/15
P-zero tran noiseless 4308 (6220)1844 (2336)3387 (4486)2570 (1828)2526 (1743)2430 (2509)2381 (2655)1/15
PRCGA sawyerr noiseless 2.4 (1)16 (18)19 (24)18 (16)18 (29)23 (36)23 (25)9/15
SMAC-BBOB hutter noiseless 2.3 (4)3000/15
U-DCN tran noiseless 4.4 (2)430 (611)574 (491)436 (369)429 (814)421 (775)720 (750)3/15
U-zero tran noiseless 10 (23)356 (171)836 (1194)639 (1268)637 (1365)1116 (3064)3e60/15
fmincon pal noiseless 3.1 (0.9)4.3 (4)7.7 (12)5.8 (7)5.7 (10)5.5 (9)5.4 (4)7/15
fminunc pal noiseless 2.8 (3)3.4 (4)14 (22)11 (10)11 (10)10 (9)10 (7)5/15
lmm-CMA-ES auger noiseless 1.3 (1)0.74 (0.5)0.79 (0.7)0.60 (1)0.59 (0.5)0.57 (0.8)0.56 (0.5)5/15
simplex pal noiseless 4.7 (3)5.9 (3)14 (5)11 (13)11 (13)10 (10)10 (17)5/15
tany liao noiseless 1.1 (0.4)1.8 (2)1.4 (1)1.1 (0.9)1.1 (0.8)1.1 (0.8)1.1 (1.0)15/15
texp liao noiseless 2.2 (4)2.1 (1)2.1 (2)1.7 (1)1.7 (1)1.7 (1)1.6 (1)15/15

Δ fopt
f16, 3-D
1e1
41
1e0
319
1e-1
582
1e-2
789
1e-3
1864
1e-5
3204
1e-7
3361
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.9 (1)2.0 (3)2.4 (1)3.1 (3)1.4 (1)0.86 (0.9)0.86 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 2.3 (1)3.1 (5)2.8 (3)3.2 (4)1.4 (1)0.93 (0.9)1.1 (1)15/15
CGA-grid100 holtschulte noiseless 1.5 (1)14 (14)300 (182)830 (1283)2e50/15
CGA-grid16 holtschulte noiseless 1.2 (1)16 (37)73 (96)842 (1521)579 (806)2e50/15
CGA-ring100 holtschulte noiseless 1.3 (2)7.2 (8)23 (12)114 (188)136 (218)2e50/15
CGA-ring16 holtschulte noiseless 1.2 (1)2.9 (4)76 (75)305 (622)2e50/15
CMAES Hutter hutter noiseless 1.1 (0.5)1.1 (0.5)1.9 (1)2.9 (2)2.4 (2)3030/15
DE Pal pal noiseless 1.2 (2)4.4 (4)9.2 (6)12 (9)7.9 (1)4.9 (2)4.8 (3)14/15
GA-100 holtschulte noiseless 1.9 (2)4.6 (6)194 (348)803 (1015)1146 (1046)2e50/15
HCMA loshchilov noiseless 1.3 (2)3.4 (6)3.2 (3)2.8 (3)1.2 (1)0.78 (0.9)0.79 (0.6)15/15
HILL holtschulte noiseless 1.4 (2)10 (11)98 (127)305 (302)529 (1207)2e50/15
HMLSL pal noiseless 3.0 (3)6.4 (4)18 (13)55 (20)37 (19)25 (20)24 (11)9/15
IP-10DDr liao noiseless 1.1 (0.6)2.0 (3)2.1 (3)2.6 (1)2.3 (5)1.4 (1)1.4 (2)15/15
IP-500 liao noiseless 1.1 (1)2.0 (4)2.1 (3)2.6 (2)117 (0.9)68 (1)65 (447)14/15
IPOP400D auger noiseless 1.4 (2)3.5 (6)3.2 (3)4.7 (3)3.2 (5)1.9 (4)1.8 (0.6)4/15
IP liao noiseless 1.1 (0.8)2.0 (0.5)2.1 (2)2.6 (5)6.0 (2)3.7 (0.5)3.6 (1)15/15
MEMPSODE voglis noiseless 2.0 (4)16 (17)17 (13)20 (6)11 (8)8.1 (4)9.0 (6)15/15
MLSL pal noiseless 3.3 (3)5.0 (8)40 (42)171 (285)4e40/15
OQNLP pal noiseless 5.0 (4)11 (13)26 (24)164 (168)69 (56)84250/15
P-DCN tran noiseless 0.92 (1.0)680 (4711)715 (2374)552 (90)445 (805)1289 (1634)5864 (6721)2/15
P-zero tran noiseless 3.1 (10)4797 (2e4)3110 (5156)2493 (4900)1329 (2012)2925 (2148)6427 (8033)1/15
PRCGA sawyerr noiseless 1.7 (1)4.8 (0.6)21 (44)54 (124)37 (66)39 (64)54 (104)8/15
SMAC-BBOB hutter noiseless 0.64 (0.6)0.68 (1.0)3.7 (3)3000/15
U-DCN tran noiseless 1.0 (1)18 (61)40 (44)2078 (3234)6725 (8662)3e60/15
U-zero tran noiseless 1.2 (1)3.7 (6)237 (455)2002 (3198)4928 (6473)3e60/15
fmincon pal noiseless 3.3 (3)7.0 (6)24 (23)133 (124)316 (413)4e40/15
fminunc pal noiseless 4.6 (4)21 (12)66 (49)784 (706)4e40/15
lmm-CMA-ES auger noiseless 1.4 (1)2.1 (3)2.3 (2)2.0 (2)0.93 (0.8)0.69 (0.6)0.68 (0.3)8/15
simplex pal noiseless 7.3 (4)2.9 (3)7.6 (6)15 (13)10 (4)11 (12)15 (13)9/15
tany liao noiseless 1.5 (0.7)3.0 (5)2.9 (3)2.3 (2)1.0 (1)0.67 (0.3)0.67 (0.6)15/15
texp liao noiseless 2.2 (3)3.0 (2)2.3 (2)1.9 (2)0.87 (0.8)0.61 (0.2)0.63 (0.6)15/15

Δ fopt
f17, 3-D
1e1
4.0
1e0
78
1e-1
282
1e-2
491
1e-3
1134
1e-5
2347
1e-7
3469
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.4 (1)4.2 (10)1.6 (0.2)1.6 (0.6)0.80 (0.5)1.0 (0.6)1.0 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 4.9 (8)3.0 (6)2.1 (2)2.5 (1)1.5 (1)1.6 (2)1.6 (0.4)15/15
CGA-grid100 holtschulte noiseless 2.8 (0.9)20 (9)160 (257)2210 (2368)2e50/15
CGA-grid16 holtschulte noiseless 2.9 (3)33 (100)206 (235)1436 (2264)2e50/15
CGA-ring100 holtschulte noiseless 3.2 (3)11 (2)35 (22)158 (117)2e50/15
CGA-ring16 holtschulte noiseless 2.1 (2)5.3 (4)87 (146)298 (153)963 (937)2e50/15
CMAES Hutter hutter noiseless 2.4 (4)1.4 (1.0)0.95 (1.0)3.0 (2)3030/15
DE Pal pal noiseless 2.5 (4)2.6 (1.0)2.6 (1)2.8 (0.5)1.8 (0.5)1.6 (0.4)1.5 (0.7)15/15
GA-100 holtschulte noiseless 3.0 (3)7.6 (5)17 (13)315 (190)2e50/15
HCMA loshchilov noiseless 3.8 (3)2.0 (1)2.0 (3)2.2 (2)1.5 (2)1.7 (1)1.6 (2)15/15
HILL holtschulte noiseless 5.0 (4)141 (482)118 (23)450 (668)1962 (1587)2e50/15
HMLSL pal noiseless 20 (12)17 (22)14 (11)13 (12)7.9 (5)5.1 (2)7.0 (9)13/15
IP-10DDr liao noiseless 2.2 (2)2.9 (7)1.5 (2)1.6 (2)1.2 (2)1.3 (0.2)1.2 (0.4)15/15
IP-500 liao noiseless 2.2 (2)2.9 (14)1.5 (2)1.6 (2)1.2 (2)1.3 (0.2)1.2 (0.5)15/15
IPOP400D auger noiseless 1.1 (1)1.2 (0.4)1.3 (0.1)1.8 (3)0.96 (4)2.7 (3)4.1 (8)2/15
IP liao noiseless 2.2 (2)2.9 (8)1.5 (2)1.6 (1)1.2 (2)1.3 (0.7)1.2 (0.5)15/15
MEMPSODE voglis noiseless 2.9 (4)30 (20)22 (9)20 (6)13 (5)10 (2)15 (9)15/15
MLSL pal noiseless 21 (41)53 (67)274 (431)6e40/15
OQNLP pal noiseless 13 (16)7.0 (6)26 (34)62 (51)110 (132)89290/15
P-DCN tran noiseless 2.2 (1)6146 (27)9893 (2e4)5687 (1e4)2496 (4000)8339 (8940)3e60/15
P-zero tran noiseless 2.1 (3)1.9e4 (4e4)2.1e4 (3e4)1.2e4 (2e4)7359 (6636)3e60/15
PRCGA sawyerr noiseless 1.3 (0.6)2.8 (1)15 (28)30 (20)29 (96)20 (36)20 (20)13/15
SMAC-BBOB hutter noiseless 1.7 (2)2.2 (4)3000/15
U-DCN tran noiseless 2.0 (2)7.3 (4)2122 (5326)6059 (4206)8260 (1e4)3e60/15
U-zero tran noiseless 2.1 (2)33 (13)2147 (2750)1.8e4 (2e4)1.8e4 (9259)3e60/15
fmincon pal noiseless 19 (30)100 (68)248 (315)5e40/15
fminunc pal noiseless 9.0 (5)7.8 (5)493 (932)3e40/15
lmm-CMA-ES auger noiseless 0.85 (1)1.5 (1)0.92 (1)1.1 (1)0.67 (1)0.52 (0.6)0.56 (0.6)10/15
simplex pal noiseless 22 (27)21 (20)132 (87)211 (403)3e40/15
tany liao noiseless 2.7 (3)1.2 (0.4)1.7 (0.3)1.5 (0.2)0.89 (0.4)0.89 (0.5)0.97 (0.6)15/15
texp liao noiseless 18 (92)3.5 (6)2.3 (2)2.2 (1.0)1.5 (0.7)0.99 (0.2)0.83 (0.1)15/15

Δ fopt
f18, 3-D
1e1
40
1e0
145
1e-1
1289
1e-2
3084
1e-3
3523
1e-5
4738
1e-7
5527
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.1 (1)2.2 (3)0.64 (0.8)0.48 (0.2)0.68 (0.5)0.71 (0.3)0.67 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 1.3 (0.9)2.7 (3)1.2 (0.7)0.63 (0.4)0.68 (0.4)0.97 (0.4)1.4 (1)15/15
CGA-grid100 holtschulte noiseless 4.7 (7)254 (492)2e50/15
CGA-grid16 holtschulte noiseless 5.2 (11)324 (1290)528 (724)2e50/15
CGA-ring100 holtschulte noiseless 6.3 (7)27 (22)56 (63)345 (450)2e50/15
CGA-ring16 holtschulte noiseless 3.6 (1)10 (8)208 (175)2e50/15
CMAES Hutter hutter noiseless 1.3 (0.8)2.2 (2)1.7 (3)3030/15
DE Pal pal noiseless 1.8 (2)3.5 (2)1.2 (0.4)0.90 (0.3)1.1 (0.4)2.3 (4)2.3 (3)14/15
GA-100 holtschulte noiseless 2.9 (2)25 (97)72 (122)328 (254)2e50/15
HCMA loshchilov noiseless 1.5 (1)2.1 (0.7)1.1 (0.7)0.75 (0.7)0.76 (0.6)1.1 (0.4)1.3 (0.3)15/15
HILL holtschulte noiseless 2.9 (6)138 (352)787 (825)2e50/15
HMLSL pal noiseless 8.5 (10)15 (11)4.7 (2)3.2 (2)3.9 (2)5.0 (4)5.2 (4)14/15
IP-10DDr liao noiseless 3.1 (15)6.5 (14)1.2 (1.0)1.2 (0.7)1.1 (0.6)0.96 (0.4)0.90 (0.5)15/15
IP-500 liao noiseless 3.1 (0.8)6.5 (14)1.2 (2)1.2 (0.7)1.1 (0.8)0.96 (0.6)0.90 (0.5)15/15
IPOP400D auger noiseless 1.0 (1)3.3 (0.6)1.3 (2)1.6 (0.9)1.8 (1)3.0 (3)2.6 (2)2/15
IP liao noiseless 3.1 (8)6.5 (11)1.2 (0.8)1.2 (0.7)1.1 (0.7)0.96 (0.6)0.90 (0.4)15/15
MEMPSODE voglis noiseless 14 (26)34 (36)19 (29)11 (11)11 (8)11 (5)23 (14)15/15
MLSL pal noiseless 10 (5)109 (95)5e40/15
OQNLP pal noiseless 7.8 (2)18 (4)13 (8)91120/15
P-DCN tran noiseless 36 (2)1.0e4 (2e4)4657 (5819)2027 (1745)5548 (4045)3e60/15
P-zero tran noiseless 37 (266)1.8e4 (3e4)1.5e4 (2e4)1.4e4 (1e4)1.2e4 (1e4)3e60/15
PRCGA sawyerr noiseless 2.0 (3)45 (120)35 (86)45 (35)136 (93)220 (209)406 (170)1/15
SMAC-BBOB hutter noiseless 1.1 (0.5)10 (11)3000/15
U-DCN tran noiseless 2.8 (3)1546 (4206)3147 (4858)3e60/15
U-zero tran noiseless 2.3 (3)822 (1669)3073 (4655)6697 (1e4)1.2e4 (2e4)3e60/15
fmincon pal noiseless 8.2 (11)168 (189)572 (801)5e40/15
fminunc pal noiseless 4.9 (2)70 (50)3e40/15
lmm-CMA-ES auger noiseless 0.75 (0.3)1.8 (2)0.94 (2)0.74 (0.4)0.77 (0.7)0.64 (1)0.96 (0.7)5/15
simplex pal noiseless 9.2 (14)31 (28)40 (19)4e40/15
tany liao noiseless 1.6 (0.8)3.0 (1)1.7 (0.9)1.3 (1)1.3 (0.8)1.1 (0.7)1.0 (0.4)15/15
texp liao noiseless 1.5 (0.3)4.7 (9)2.2 (2)1.7 (0.5)1.6 (0.6)1.4 (0.4)1.3 (0.4)15/15

Δ fopt
f19, 3-D
1e1
1
1e0
1
1e-1
109
1e-2
6764
1e-3
7367
1e-5
7399
1e-7
7441
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 8.0 (5)676 (775)57 (92)3.7 (2)4.6 (5)4.6 (4)4.6 (7)15/15
BIPOP-saACM-k loshchilov noiseless 6.5 (7)247 (562)40 (62)2.3 (2)2.7 (3)2.7 (2)2.7 (3)15/15
CGA-grid100 holtschulte noiseless 11 (9)590 (1000)123 (68)69 (68)143 (83)286 (431)2e50/15
CGA-grid16 holtschulte noiseless 5.7 (7)466 (449)217 (487)42 (45)73 (42)2e50/15
CGA-ring100 holtschulte noiseless 7.1 (8)451 (219)77 (63)21 (20)67 (112)293 (598)2e50/15
CGA-ring16 holtschulte noiseless 11 (10)319 (306)48 (73)16 (15)47 (46)289 (426)2e50/15
CMAES Hutter hutter noiseless 10 (10)150 (127)41 (22)3030/15
DE Pal pal noiseless 11 (8)191 (180)22 (19)2.9 (4)6.2 (6)7.4 (9)7.5 (16)9/15
GA-100 holtschulte noiseless 4.9 (4)373 (340)58 (36)13 (15)51 (52)302 (253)2e50/15
HCMA loshchilov noiseless 9.3 (8)126 (160)38 (61)2.4 (1)2.7 (2)2.8 (1)2.8 (3)15/15
HILL holtschulte noiseless 13 (11)531 (168)81 (151)96 (249)139 (102)140 (109)297 (423)0/15
HMLSL pal noiseless 1 (0)1 (0)0.16 (0)10 (11)14 (6)16 (22)16 (19)6/15
IP-10DDr liao noiseless 10 (20)179 (184)152 (179)7.5 (4)10 (8)10 (8)10 (13)15/15
IP-500 liao noiseless 10 (11)179 (258)152 (276)5.7 (9)7.0 (6)7.0 (4)7.0 (8)15/15
IPOP400D auger noiseless 1 (0)1 (0)27 (24)4.2 (2)3.9 (5)3.9 (2)3.9 (4)1/15
IP liao noiseless 10 (7)179 (196)152 (255)5.7 (4)7.0 (5)7.0 (8)7.0 (5)15/15
MEMPSODE voglis noiseless 14 (12)1190 (806)78 (22)5.7 (9)24 (21)24 (7)25 (12)14/15
MLSL pal noiseless 1 (0)1 (0)0.16 (0)29 (33)36 (64)36 (28)36 (41)3/15
OQNLP pal noiseless 1 (0)1 (0)0.11 (0)★40.80 (0.6)1.6 (2)1.6 (2)2.0 (2)5/15
P-DCN tran noiseless 16 (7)407 (284)171 (284)1263 (1855)2724 (1768)2726 (2433)2761 (3417)2/15
P-zero tran noiseless 12 (8)946 (1072)2391 (2333)2884 (3659)3e60/15
PRCGA sawyerr noiseless 4.5 (2)108 (55)12 (25)7.4 (13)10 (8)34 (32)61 (105)3/15
SMAC-BBOB hutter noiseless 1 (0)1 (0)3000/15
U-DCN tran noiseless 12 (6)360 (533)354 (115)255 (227)391 (235)1313 (877)5820 (1e4)0/15
U-zero tran noiseless 9.2 (8)268 (394)306 (69)369 (1072)1302 (3360)5850 (5676)3e60/15
fmincon pal noiseless 1 (0)1 (0)0.16 (0)31 (58)59 (54)59 (88)59 (56)2/15
fminunc pal noiseless 1 (0)1 (0)0.16 (0)4.8 (5)8.3 (3)8.3 (8)8.2 (8)8/15
lmm-CMA-ES auger noiseless 1 (0)1 (0)27 (27)1.4 (1)2.0 (3)2.0 (2)2.0 (3)2/15
simplex pal noiseless 1 (0)1 (0)0.14 (0.0)3.5 (3)14 (19)14 (14)14 (10)6/15
tany liao noiseless 7.3 (11)157 (165)178 (362)10 (18)11 (10)11 (13)11 (16)15/15
texp liao noiseless 2.7 (2)60 (64)136 (48)7.2 (8)7.5 (8)7.5 (9)7.5 (8)15/15

Δ fopt
f20, 3-D
1e1
8.0
1e0
385
1e-1
2291
1e-2
2398
1e-3
2481
1e-5
2573
1e-7
2776
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.5 (2)3.2 (4)6.9 (5)6.8 (5)6.7 (6)6.7 (6)6.3 (7)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (2)2.1 (2)3.6 (6)3.8 (6)3.7 (6)3.6 (3)3.3 (5)15/15
CGA-grid100 holtschulte noiseless 6.3 (12)8.0 (7)58 (63)111 (147)419 (338)2e50/15
CGA-grid16 holtschulte noiseless 3.4 (4)4.0 (3)41 (44)62 (101)92 (108)870 (816)2e50/15
CGA-ring100 holtschulte noiseless 4.2 (6)6.3 (2)5.2 (3)9.3 (4)19 (5)122 (75)2e50/15
CGA-ring16 holtschulte noiseless 6.2 (9)2.2 (0.8)18 (82)19 (3)22 (31)74 (38)787 (581)0/15
CMAES Hutter hutter noiseless 2.8 (2)2.6 (3)3030/15
DE Pal pal noiseless 5.2 (3)2.0 (2)31 (26)29 (32)29 (73)28 (18)26 (27)7/15
GA-100 holtschulte noiseless 7.7 (13)3.9 (3)6.8 (17)9.2 (32)16 (9)102 (262)2e50/15
HCMA loshchilov noiseless 1.2 (0.3)4.2 (5)3.2 (2)3.1 (3)3.1 (3)3.1 (3)2.9 (3)15/15
HILL holtschulte noiseless 5.6 (4)8.2 (26)27 (53)27 (51)30 (46)103 (134)803 (581)0/15
HMLSL pal noiseless 2.0 (0)1.6 (0.9)14 (20)13 (13)13 (24)12 (12)11 (16)10/15
IP-10DDr liao noiseless 4.0 (1)4.6 (4)15 (11)14 (11)14 (11)13 (10)12 (5)15/15
IP-500 liao noiseless 4.0 (2)4.6 (4)10 (0.3)10 (3)10 (3)10 (0.8)10 (0.7)15/15
IPOP400D auger noiseless 1.2 (1)10 (13)20070/15
IP liao noiseless 4.0 (1)4.6 (4)10 (0.8)10 (1)10 (3)10 (0.6)10 (2)15/15
MEMPSODE voglis noiseless 4.6 (3)7.0 (6)15 (4)14 (19)14 (14)13 (24)13 (16)15/15
MLSL pal noiseless 2.0 (0)1.5 (1.0)2.4 (4)2.3 (3)2.2 (2)2.2 (2)2.0 (2)15/15
OQNLP pal noiseless 1.9 (0)2.0 (2)5.0 (6)4.8 (6)4.6 (3)4.4 (7)4.1 (7)4/15
P-DCN tran noiseless 4.4 (4)485 (1782)1.9e4 (2e4)1.8e4 (1e4)1.8e4 (2e4)1.7e4 (2e4)1.6e4 (1e4)1/15
P-zero tran noiseless 7.7 (6)3221 (3609)6083 (5565)5812 (6700)5618 (8162)5418 (5370)5041 (5684)2/15
PRCGA sawyerr noiseless 1.7 (1)8.1 (4)21 (26)21 (25)21 (39)21 (15)21 (26)14/15
SMAC-BBOB hutter noiseless 0.99 (0.5)5.7 (5)3000/15
U-DCN tran noiseless 3.7 (2)8.7 (28)376 (1680)360 (958)348 (66)345 (339)389 (811)7/15
U-zero tran noiseless 2.8 (2)30 (79)258 (304)247 (287)247 (383)331 (272)1942 (2222)0/15
fmincon pal noiseless 2.0 (0)1.6 (1)5.9 (5)5.7 (7)5.5 (2)5.3 (3)4.9 (4)13/15
fminunc pal noiseless 1.1 (0)2.2 (2)6.0 (7)5.8 (8)5.6 (2)5.4 (12)5.0 (0.9)13/15
lmm-CMA-ES auger noiseless 1.5 (0.9)8.6 (12)13 (15)12 (7)12 (5)12 (5)11 (17)1/15
simplex pal noiseless 6.0 (2)3.6 (1)9.3 (16)8.9 (8)8.6 (9)8.3 (7)7.7 (11)12/15
tany liao noiseless 3.1 (1)8.5 (6)15 (16)15 (16)14 (15)14 (15)13 (13)15/15
texp liao noiseless 0.99 (0.4)2.5 (1)21 (25)21 (24)21 (22)20 (21)19 (15)15/15

Δ fopt
f21, 3-D
1e1
6.0
1e0
184
1e-1
425
1e-2
439
1e-3
458
1e-5
469
1e-7
482
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 2.5 (3)8.1 (12)12 (3)12 (44)12 (44)12 (26)12 (26)15/15
BIPOP-saACM-k loshchilov noiseless 1.0 (0.7)8.6 (33)7.8 (11)7.8 (14)7.6 (11)7.5 (16)7.4 (12)15/15
CGA-grid100 holtschulte noiseless 1.3 (2)10 (5)30 (180)47 (113)105 (221)284 (347)815 (484)4/15
CGA-grid16 holtschulte noiseless 1.1 (2)2.4 (3)11 (9)20 (36)29 (28)91 (91)240 (233)7/15
CGA-ring100 holtschulte noiseless 1.5 (2)4.0 (5)3.1 (3)7.6 (8)11 (6)34 (8)158 (145)11/15
CGA-ring16 holtschulte noiseless 1.5 (0.9)4.1 (18)3.5 (0.8)4.5 (17)6.6 (6)22 (14)83 (50)15/15
CMAES Hutter hutter noiseless 2.1 (2)2.2 (3)1.7 (1)1.7 (1)1.7 (2)1.7 (0.8)1.7 (2)5/15
DE Pal pal noiseless 2.1 (3)2.2 (1)23 (0.5)22 (69)22 (0.6)22 (0.9)22 (31)13/15
GA-100 holtschulte noiseless 0.86 (0.5)3.0 (3)3.1 (2)5.0 (2)7.1 (4)15 (1)38 (21)15/15
HCMA loshchilov noiseless 2.2 (1)3.3 (7)7.5 (3)7.9 (4)7.8 (21)7.9 (20)7.7 (5)15/15
HILL holtschulte noiseless 5.5 (9)186 (310)130 (125)126 (77)122 (169)127 (37)169 (278)12/15
HMLSL pal noiseless 4.1 (6)2.4 (2)1.7 (0.5)1.8 (0.9)1.7 (2)1.8 (0.8)1.8 (1.0)15/15
IP-10DDr liao noiseless 1.6 (1)4.9 (3)9.5 (15)12 (16)11 (15)11 (14)11 (15)15/15
IP-500 liao noiseless 1.6 (1)4.9 (3)18 (46)44 (105)62 (29)62 (154)61 (109)15/15
IPOP400D auger noiseless 2.0 (1)5.3 (5)3.3 (7)3.3 (3)3.3 (3)3.3 (5)3.4 (6)10/15
IP liao noiseless 1.6 (2)4.9 (9)15 (32)38 (54)131 (37)221 (64)217 (57)15/15
MEMPSODE voglis noiseless 2.3 (3)7.8 (5)18 (51)19 (49)18 (46)18 (7)25 (7)15/15
MLSL pal noiseless 4.0 (5)1.2 (0.5)1.5 (2)1.5 (2)1.4 (2)1.4 (2)1.5 (0.4)15/15
OQNLP pal noiseless 4.0 (4)1.5 (3)1.8 (2)1.9 (4)1.8 (1)1.8 (0.8)2.4 (2)13/15
P-DCN tran noiseless 1.5 (2)3.3e4 (5e4)4.6e4 (5e4)4.4e4 (4e4)4.3e4 (7e4)4.2e4 (5e4)4.0e4 (2e4)2/15
P-zero tran noiseless 1.4 (2)1.9e4 (2e4)1.4e4 (2e4)1.4e4 (2e4)1.3e4 (1e4)1.3e4 (2e4)1.2e4 (3e4)5/15
PRCGA sawyerr noiseless 0.71 (1)9.2 (0.8)15 (17)18 (27)27 (29)41 (42)47 (46)15/15
SMAC-BBOB hutter noiseless 1.2 (2)0.74 (0.5)0.56 (0.5)1.3 (0.5)2.4 (1)3000/15
U-DCN tran noiseless 1.2 (1)2.9 (4)2.9 (2)4.1 (4)6.2 (4)15 (8)32 (28)15/15
U-zero tran noiseless 0.98 (1)7.5 (3)11 (14)13 (22)17 (12)40 (53)119 (142)15/15
fmincon pal noiseless 4.3 (5)1.6 (1.0)1.1 (1)1.1 (0.6)1.1 (1)1.1 (1)1.2 (0.7)15/15
fminunc pal noiseless 4.6 (6)1.9 (0.7)1.7 (1)1.7 (0.7)1.6 (0.9)1.7 (1)1.7 (0.8)15/15
lmm-CMA-ES auger noiseless 2.2 (2)2.1 (4)2.2 (3)2.6 (6)2.5 (4)2.6 (2)2.8 (4)10/15
simplex pal noiseless 19 (11)2.4 (1.0)1.6 (1)1.6 (2)1.6 (1)1.6 (1)1.6 (0.7)15/15
tany liao noiseless 1.1 (1)4.9 (6)9.5 (22)10 (10)10 (5)10 (15)10 (16)15/15
texp liao noiseless 1.3 (1)4.9 (10)8.6 (12)10 (13)10 (11)10 (12)10 (10)15/15

Δ fopt
f22, 3-D
1e1
18
1e0
170
1e-1
354
1e-2
362
1e-3
384
1e-5
401
1e-7
414
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.4 (0.8)6.9 (7)11 (7)12 (18)15 (16)14 (15)14 (19)15/15
BIPOP-saACM-k loshchilov noiseless 2.4 (5)4.5 (4)15 (34)15 (30)15 (32)14 (10)14 (8)15/15
CGA-grid100 holtschulte noiseless 1.7 (2)2.7 (2)41 (115)109 (265)154 (258)935 (608)2593 (2277)2/15
CGA-grid16 holtschulte noiseless 1.8 (3)7.4 (4)83 (249)138 (311)167 (196)323 (242)880 (543)3/15
CGA-ring100 holtschulte noiseless 2.0 (2)3.3 (3)4.6 (5)8.3 (5)43 (11)194 (290)377 (421)8/15
CGA-ring16 holtschulte noiseless 3.0 (4)4.2 (5)92 (7)96 (151)106 (212)343 (312)516 (275)3/15
CMAES Hutter hutter noiseless 3.0 (6)1.7 (2)2.0 (1)2.0 (5)2.6 (2)5.4 (6)5.4 (5)2/15
DE Pal pal noiseless 1.4 (1)56 (265)86 (86)85 (125)81 (157)79 (225)77 (73)10/15
GA-100 holtschulte noiseless 1.7 (2)65 (2)39 (23)55 (85)127 (121)239 (210)424 (660)8/15
HCMA loshchilov noiseless 1.3 (1)3.5 (8)12 (10)23 (11)22 (10)27 (7)26 (68)15/15
HILL holtschulte noiseless 2.1 (2)298 (442)335 (526)358 (360)427 (488)796 (670)1621 (1716)2/15
HMLSL pal noiseless 2.3 (2)1.7 (1)1.4 (0.8)1.4 (0.9)1.4 (1)1.4 (1)1.5 (1)15/15
IP-10DDr liao noiseless 1.7 (0.7)3.4 (8)11 (30)47 (12)45 (132)43 (215)42 (112)15/15
IP-500 liao noiseless 1.7 (2)3.4 (13)41 (29)108 (245)163 (27)1578 (3751)1824 (27)12/15
IPOP400D auger noiseless 2.0 (2)8.5 (12)40 (61)40 (63)38 (51)36 (38)35 (40)2/15
IP liao noiseless 1.7 (2)3.4 (8)37 (15)101 (234)351 (27)1883 (3741)1824 (1832)12/15
MEMPSODE voglis noiseless 1.2 (0.8)17 (6)23 (25)24 (43)22 (40)22 (36)21 (33)15/15
MLSL pal noiseless 2.0 (3)1.3 (0.7)1.7 (2)1.7 (2)1.6 (0.9)1.6 (2)1.8 (2)15/15
OQNLP pal noiseless 3.0 (3)3.3 (2)1.8 (4)1.8 (3)1.7 (0.3)1.7 (3)2.9 (2)10/15
P-DCN tran noiseless 2.0 (3)1.2e4 (1e4)2.3e4 (5e4)2.3e4 (4e4)2.1e4 (3e4)2.1e4 (3e4)2.0e4 (1e4)4/15
P-zero tran noiseless 2.3 (6)3.5e4 (1e4)5.5e4 (5e4)5.4e4 (3e4)5.1e4 (5e4)4.9e4 (4e4)4.7e4 (9e4)2/15
PRCGA sawyerr noiseless 1.5 (2)9.4 (46)31 (63)59 (18)69 (104)113 (160)129 (122)15/15
SMAC-BBOB hutter noiseless 0.80 (0.7)0.58 (0.4)1.4 (2)2.1 (2)5.3 (9)3000/15
U-DCN tran noiseless 1.4 (2)2.3 (6)4.3 (4)21 (5)51 (140)180 (357)587 (1193)14/15
U-zero tran noiseless 1.8 (2)3.5 (3)5.3 (6)106 (311)136 (133)1871 (1049)3730 (7383)9/15
fmincon pal noiseless 2.4 (0.3)1.1 (0.8)0.93 (0.4)0.96 (0.1)0.96 (0.9)1.00 (0.6)1.1 (0.3)15/15
fminunc pal noiseless 1.8 (4)1.2 (0.9)0.86 (0.8)0.90 (0.5)0.90 (0.5)0.98 (0.3)1.1 (0.5)15/15
lmm-CMA-ES auger noiseless 1.3 (1)5.1 (9)10 (6)13 (14)12 (9)12 (14)11 (9)5/15
simplex pal noiseless 10 (9)3.3 (2)1.9 (0.2)2.0 (0.7)1.9 (0.7)1.8 (1)1.8 (1.0)15/15
tany liao noiseless 1.4 (1)8.3 (8)20 (20)39 (11)58 (152)60 (183)58 (66)15/15
texp liao noiseless 5.1 (3)11 (25)12 (20)12 (9)11 (18)11 (5)11 (17)15/15

Δ fopt
f23, 3-D
1e1
3.0
1e0
407
1e-1
906
1e-2
1215
1e-3
2214
1e-5
2293
1e-7
2393
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.1 (3)5.2 (3)5.3 (4)4.3 (2)2.4 (2)2.5 (2)2.5 (1)15/15
BIPOP-saACM-k loshchilov noiseless 3.0 (3)7.9 (10)5.8 (6)5.2 (4)2.9 (2)3.1 (2)3.3 (3)15/15
CGA-grid100 holtschulte noiseless 3.6 (3)22 (18)2439 (1656)2e50/15
CGA-grid16 holtschulte noiseless 2.8 (4)20 (15)1201 (1407)2e50/15
CGA-ring100 holtschulte noiseless 2.8 (2)33 (39)2412 (1407)2e50/15
CGA-ring16 holtschulte noiseless 3.6 (2)9.4 (10)1192 (1090)2e50/15
CMAES Hutter hutter noiseless 3.2 (3)3030/15
DE Pal pal noiseless 3.6 (4)6.3 (4)18 (6)21 (5)13 (3)13 (3)13 (3)15/15
GA-100 holtschulte noiseless 4.1 (4)23 (19)1195 (1076)2e50/15
HCMA loshchilov noiseless 6.4 (4)5.3 (6)6.1 (7)5.0 (4)3.2 (2)3.3 (3)3.5 (3)15/15
HILL holtschulte noiseless 5.5 (7)15 (29)2420 (3808)2e50/15
HMLSL pal noiseless 12 (11)1.7 (2)3.7 (5)3.0 (4)4.2 (14)6e40/15
IP-10DDr liao noiseless 3.3 (4)5.2 (4)6.8 (11)5.2 (1)2.9 (4)3.0 (1)3.0 (3)15/15
IP-500 liao noiseless 3.3 (3)5.2 (4)6.8 (9)5.2 (8)2.9 (3)3.0 (4)3.0 (2)15/15
IPOP400D auger noiseless 3.6 (4)5.1 (5)7.2 (9)5.5 (6)4.3 (6)4.2 (2)6.1 (8)2/15
IP liao noiseless 3.3 (3)5.2 (4)6.8 (5)5.2 (7)2.9 (3)3.0 (1)3.0 (0.7)15/15
MEMPSODE voglis noiseless 2.3 (3)3.8 (4)8.6 (11)8.5 (6)5.0 (3)6.0 (6)5.7 (3)15/15
MLSL pal noiseless 13 (6)1.2 (1)2.7 (3)4.8 (11)4.1 (3)150 (241)5e40/15
OQNLP pal noiseless 12 (2)2.1 (2)16 (20)27 (31)42 (60)1e40/15
P-DCN tran noiseless 3.1 (4)6.7 (17)1299 (3339)1.0e4 (2e4)2.0e4 (2e4)3e60/15
P-zero tran noiseless 3.3 (4)15 (83)1215 (1983)1.6e4 (3e4)3e60/15
PRCGA sawyerr noiseless 3.9 (4)7.5 (7)31 (33)85 (98)99 (101)153 (179)151 (181)4/15
SMAC-BBOB hutter noiseless 3.0 (2)3000/15
U-DCN tran noiseless 2.5 (1)11 (19)4413 (9831)3e60/15
U-zero tran noiseless 2.3 (2)24 (29)4660 (3090)3e60/15
fmincon pal noiseless 11 (7)0.95 (0.7)2.4 (3)4.2 (2)4.4 (7)50 (50)5e40/15
fminunc pal noiseless 10 (13)3.0 (3)66 (121)4e40/15
lmm-CMA-ES auger noiseless 4.8 (10)2.5 (3)3.7 (4)4.0 (2)2.2 (2)2.2 (2)2.1 (3)5/15
simplex pal noiseless 69 (104)2.0 (1)2.1 (1)1.9 (1)1.4 (2)1.5 (1)1.5 (2)15/15
tany liao noiseless 2.5 (3)7.1 (4)7.4 (4)5.7 (4)3.2 (2)3.3 (1)3.3 (2)15/15
texp liao noiseless 3.2 (4)4.3 (5)4.4 (2)3.5 (6)2.0 (0.9)2.1 (1)2.1 (0.8)15/15

Δ fopt
f24, 3-D
1e1
97
1e0
10391
1e-1
1.0e5
1e-2
3.6e5
1e-3
3.6e5
1e-5
3.6e5
1e-7
3.6e5
#succ
2/15
BIPOP-aCMA-STEP loshchilov noiseless 2.2 (1)6.2 (3)9.0 (17)5.2 (3)7.3 (9)7.3 (8)7.3 (14)10/15
BIPOP-saACM-k loshchilov noiseless 1.6 (1)3.3 (3)9.0 (11)5.7 (2)7.2 (7)7.2 (7)8.2 (8)10/15
CGA-grid100 holtschulte noiseless 8.5 (7)210 (69)2e50/15
CGA-grid16 holtschulte noiseless 6.7 (5)101 (174)2e50/15
CGA-ring100 holtschulte noiseless 10 (5)27 (42)2e50/15
CGA-ring16 holtschulte noiseless 5.9 (5)42 (35)2e50/15
CMAES Hutter hutter noiseless 1.6 (2)3030/15
DE Pal pal noiseless 3.1 (1)24 (21)3.9 (4)1.1 (2)1.1 (1)1.1 (1)1.1 (2)2/15
GA-100 holtschulte noiseless 4.6 (4)2e50/15
HCMA loshchilov noiseless 1.6 (0.7)6.5 (20)10 (16)10 (19)10 (12)10 (15)10 (14)8/15
HILL holtschulte noiseless 5.3 (6)96 (121)2e50/15
HMLSL pal noiseless 2.4 (2)10 (23)2.7 (2)0.78 (0.6)0.78 (1)0.79 (0.7)0.79 (0.7)3/15
IP-10DDr liao noiseless 2.2 (2)115 (185)136 (117)61 (59)61 (57)61 (48)61 (38)2/15
IP-500 liao noiseless 2.2 (1)3e60/15
IPOP400D auger noiseless 2.0 (4)2.8 (3)20140/15
IP liao noiseless 2.2 (2)3e60/15
MEMPSODE voglis noiseless 9.2 (7)31 (42)3.5 (2)1.0 (0.6)1.1 (0.8)1.1 (0.6)1.1 (2)14/15
MLSL pal noiseless 2.0 (1)2.2 (5)3e40/15
OQNLP pal noiseless 4.1 (1)0.67 (1)0.24 (0.2)0.17 (0.2)0.17 (0.1)0.17 (0.2)0.17 (0.1)2/15
P-DCN tran noiseless 51 (110)1159 (1443)119 (138)35 (80)35 (78)35 (36)35 (49)3/15
P-zero tran noiseless 309 (317)3e60/15
PRCGA sawyerr noiseless 2.7 (2)5.1 (6)4.5 (5)7.1 (4)2e50/15
SMAC-BBOB hutter noiseless 4.3 (5)3000/15
U-DCN tran noiseless 5.0 (3)143 (283)3e60/15
U-zero tran noiseless 4.4 (3)466 (168)3e60/15
fmincon pal noiseless 1.9 (1)2.7 (4)4e40/15
fminunc pal noiseless 3.4 (4)3.0 (4)4e40/15
lmm-CMA-ES auger noiseless 1.5 (3)0.84 (0.8)20100/15
simplex pal noiseless 5.5 (2)7.0 (2)4e40/15
tany liao noiseless 1.8 (2)57 (89)75 (79)122 (206)122 (138)122 (227)122 (88)1/15
texp liao noiseless 1.7 (0.8)2.2 (2)4.2 (2)2.4 (3)2.4 (2)2.4 (3)2.4 (1)15/15

Previous dimension | Dimension = 5 | Next dimension

Δ fopt
f1, 5-D
1e1
11
1e0
12
1e-1
12
1e-2
12
1e-3
12
1e-5
12
1e-7
12
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.1 (0.3)4.5 (0)6.0 (0)7.4 (0.6)8.5 (0.7)11 (0.2)14 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 3.7 (2)7.8 (1)10 (0.6)11 (0.7)13 (0.9)16 (1)20 (1)15/15
CGA-grid100 holtschulte noiseless 16 (22)154 (51)458 (158)1135 (761)3333 (1831)7.4e4 (8e4)2e50/15
CGA-grid16 holtschulte noiseless 11 (11)38 (24)99 (39)263 (95)641 (310)6061 (2042)3.0e5 (2e5)0/15
CGA-ring100 holtschulte noiseless 12 (14)109 (41)320 (90)662 (198)1256 (404)4291 (1044)4.8e4 (5e4)0/15
CGA-ring16 holtschulte noiseless 6.7 (7)28 (9)67 (10)154 (48)271 (132)2085 (857)4.7e4 (7e4)0/15
CMAES Hutter hutter noiseless 1.9 (1)8.4 (3)15 (2)23 (5)28 (5)66 (66)5060/15
DE Pal pal noiseless 4.9 (3)21 (7)40 (5)62 (8)80 (7)122 (11)160 (7)15/15
GA-100 holtschulte noiseless 6.1 (3)71 (40)175 (68)388 (125)882 (343)5282 (3053)1.5e5 (2e5)0/15
HCMA loshchilov noiseless 1.1 (0)1 (0)★31 (0)★41 (0)★41 (0)★41 (0)★41 (0)★415/15
HILL holtschulte noiseless 4.3 (4)8.4 (3)22 (17)62 (32)213 (81)2667 (1234)3.9e4 (1e4)0/15
HMLSL pal noiseless 0.71 (0.3)1.4 (0.5)2.1 (0)2.1 (0.1)2.6 (0.2)3.5 (0.2)3.9 (0.4)15/15
IP-10DDr liao noiseless 3.0 (1)7.6 (1)13 (3)21 (4)27 (4)41 (3)54 (6)15/15
IP-500 liao noiseless 3.0 (2)7.6 (1)13 (2)21 (4)27 (3)41 (6)54 (4)15/15
IPOP400D auger noiseless 2.2 (0.6)7.0 (3)14 (2)20 (2)25 (6)38 (2)52 (4)15/15
IP liao noiseless 3.0 (0.7)7.6 (1)13 (3)21 (3)27 (3)41 (4)54 (4)15/15
MEMPSODE voglis noiseless 5.7 (4)7.4 (0)7.4 (0)7.4 (0)7.4 (0)7.4 (0)7.6 (0.2)15/15
MLSL pal noiseless 0.71 (0.3)1.4 (0.5)2.1 (0)2.1 (0.2)2.6 (0.4)3.5 (0.2)3.9 (0.5)15/15
OQNLP pal noiseless 1.7 (0.0)1.8 (0.2)2.2 (0.4)2.4 (0.0)2.5 (0.1)2.6 (0)2.6 (0)15/15
P-DCN tran noiseless 7.5 (9)28 (17)42 (18)50 (22)65 (13)203 (35)502 (145)15/15
P-zero tran noiseless 11 (5)30 (25)41 (36)47 (28)55 (21)136 (31)675 (259)15/15
PRCGA sawyerr noiseless 4.1 (8)25 (9)49 (12)85 (50)168 (250)358 (573)1786 (3457)15/15
SMAC-BBOB hutter noiseless 0.91 (0.3)1.5 (0.3)2.4 (0.3)3.6 (0.8)121 (187)5000/15
U-DCN tran noiseless 3.1 (2)21 (4)85 (36)190 (76)373 (101)862 (305)2321 (2067)15/15
U-zero tran noiseless 3.2 (1)14 (7)55 (42)180 (134)388 (286)4106 (1234)3.9e4 (2e4)15/15
fmincon pal noiseless 0.71 (0.3)1.4 (0.5)2.1 (0)2.1 (0.1)2.6 (0.2)3.5 (0.2)3.9 (0.4)15/15
fminunc pal noiseless 1.0 (0.3)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)15/15
lmm-CMA-ES auger noiseless 1.6 (0.8)2.9 (0.6)3.6 (0.4)4.4 (0.7)5.1 (0.4)6.8 (0.5)8.5 (0.7)15/15
simplex pal noiseless 21 (40)64 (28)77 (22)84 (13)87 (8)92 (13)96 (14)15/15
tany liao noiseless 2.7 (1)7.5 (2)16 (2)24 (3)31 (2)45 (3)57 (4)15/15
texp liao noiseless 2.7 (2)6.8 (2)13 (3)21 (4)29 (2)45 (5)56 (4)15/15

Δ fopt
f2, 5-D
1e1
83
1e0
87
1e-1
88
1e-2
89
1e-3
90
1e-5
92
1e-7
94
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.4 (0.1)1.5 (0.2)1.8 (0.2)2.0 (0.2)2.2 (0.1)2.5 (0.3)2.8 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 3.6 (0.8)4.0 (0.8)4.1 (0.6)4.4 (0.8)4.6 (0.3)5.0 (0.6)5.4 (0.8)15/15
CGA-grid100 holtschulte noiseless 322 (329)1251 (2222)4920 (3676)2e50/15
CGA-grid16 holtschulte noiseless 127 (155)349 (435)948 (455)4265 (6116)2.0e4 (3e4)2e50/15
CGA-ring100 holtschulte noiseless 138 (71)241 (149)1459 (3708)2893 (3592)1.3e4 (2e4)2e50/15
CGA-ring16 holtschulte noiseless 68 (39)251 (199)716 (169)3640 (3844)6295 (4492)2e50/15
CMAES Hutter hutter noiseless 5060/15
DE Pal pal noiseless 11 (1)13 (1)15 (1)18 (1)20 (0.8)25 (2)30 (0.6)15/15
GA-100 holtschulte noiseless 89 (47)294 (323)2078 (1851)9299 (1e4)4.1e4 (1e4)2e50/15
HCMA loshchilov noiseless 1.5 (0.2)1.6 (0.2)1.8 (0.2)2.0 (0.2)2.2 (0.2)2.5 (0.2)2.8 (0.1)15/15
HILL holtschulte noiseless 95 (67)303 (362)1209 (1805)5841 (8511)1.3e4 (2e4)2e50/15
HMLSL pal noiseless 1.9 (1.0)2.1 (0.9)2.3 (0.9)2.4 (1)2.6 (1)3.9 (4)5.6 (1)15/15
IP-10DDr liao noiseless 13 (5)17 (7)19 (5)20 (2)21 (2)23 (2)24 (2)15/15
IP-500 liao noiseless 13 (5)17 (5)19 (3)20 (3)21 (2)23 (3)24 (2)15/15
IPOP400D auger noiseless 13 (3)15 (3)17 (2)18 (1)19 (2)20 (1)21 (2)15/15
IP liao noiseless 13 (4)17 (6)19 (4)20 (2)21 (2)23 (2)24 (1)15/15
MEMPSODE voglis noiseless 3.6 (2)4.2 (3)4.6 (3)4.7 (3)4.7 (3)5.0 (3)5.2 (0.9)15/15
MLSL pal noiseless 1.9 (1.0)2.1 (0.9)2.3 (1)2.4 (0.8)2.6 (1)3.7 (1)5.1 (4)15/15
OQNLP pal noiseless 2.0 (1)2.5 (1)2.6 (2)2.7 (1)2.8 (1)3.0 (1)131 (90)3/15
P-DCN tran noiseless 20 (7)28 (9)47 (18)76 (29)139 (40)212 (156)612 (430)15/15
P-zero tran noiseless 16 (8)21 (7)44 (33)120 (66)225 (157)2833 (2657)1.8e4 (2e4)7/15
PRCGA sawyerr noiseless 13 (3)38 (4)52 (94)80 (93)353 (1130)747 (165)1104 (1323)15/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 107 (109)194 (158)265 (182)397 (186)1226 (783)1344 (227)7420 (5277)12/15
U-zero tran noiseless 176 (316)783 (635)1970 (1571)7824 (7886)2.0e4 (3e4)5e60/15
fmincon pal noiseless 1.8 (1)1.8 (0.7)2.0 (1)2.1 (0.6)2.4 (1)3.1 (1)4.0 (1)15/15
fminunc pal noiseless 4.5 (2)5.8 (3)6.6 (2)6.9 (2)7.1 (2)7.4 (2)7.6 (2)15/15
lmm-CMA-ES auger noiseless 3.2 (1.0)4.0 (0.6)4.4 (1)4.6 (0.5)4.8 (1)5.0 (1.0)5.4 (1)15/15
simplex pal noiseless 19 (11)25 (9)28 (4)28 (8)28 (4)28 (3)28 (5)15/15
tany liao noiseless 15 (3)17 (2)18 (3)19 (1.0)20 (2)22 (1)23 (1)15/15
texp liao noiseless 15 (4)18 (4)20 (2)21 (2)22 (2)23 (1)24 (2)15/15

Δ fopt
f3, 5-D
1e1
716
1e0
1622
1e-1
1637
1e-2
1642
1e-3
1646
1e-5
1650
1e-7
1654
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.27 (0.0)0.29 (0.1)0.32 (0.1)0.34 (0.1)0.35 (0.1)0.39 (0.1)0.42 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1.1 (0.6)12 (14)94 (504)94 (504)94 (271)94 (259)95 (264)15/15
CGA-grid100 holtschulte noiseless 5.3 (2)19 (7)56 (16)401 (553)2e50/15
CGA-grid16 holtschulte noiseless 1.1 (0.3)4.2 (2)11 (4)35 (19)129 (92)2e50/15
CGA-ring100 holtschulte noiseless 4.4 (0.9)7.4 (2)16 (6)28 (9)56 (15)2e50/15
CGA-ring16 holtschulte noiseless 0.98 (0.3)1.9 (0.7)5.7 (3)17 (7)36 (15)2e50/15
CMAES Hutter hutter noiseless 1.2 (0.9)5060/15
DE Pal pal noiseless 1.2 (0.4)1.7 (0.3)1.9 (0.3)2.1 (0.3)2.3 (0.2)2.5 (0.3)2.8 (0.3)15/15
GA-100 holtschulte noiseless 2.3 (0.4)4.1 (0.7)11 (6)33 (10)77 (25)2257 (3523)2e50/15
HCMA loshchilov noiseless 0.29 (0.2)3.0 (2)55 (320)54 (0.1)55 (0.1)55 (160)55 (86)15/15
HILL holtschulte noiseless 0.36 (0.1)1.4 (0.6)4.6 (2)18 (18)46 (19)2e50/15
HMLSL pal noiseless 1.3 (0.4)2.2 (1)3.2 (0.8)3.2 (1)3.2 (0.7)3.3 (1)3.3 (2)15/15
IP-10DDr liao noiseless 0.99 (1)15 (17)60 (69)60 (80)60 (41)61 (46)61 (79)15/15
IP-500 liao noiseless 0.99 (0.4)18 (10)257 (409)258 (39)258 (517)259 (432)259 (80)15/15
IPOP400D auger noiseless 1.2 (2)28050/15
IP liao noiseless 0.99 (1.0)48 (11)2690 (1530)2683 (2295)2676 (6070)2671 (5311)2665 (3026)8/15
MEMPSODE voglis noiseless 3.6 (1)9.2 (6)15 (6)15 (6)15 (6)15 (6)15 (5)15/15
MLSL pal noiseless 5.6 (6)279 (736)6e40/15
OQNLP pal noiseless 8.6 (17)41 (44)1e40/15
P-DCN tran noiseless 7.5 (13)26 (33)153 (49)152 (165)152 (398)155 (108)166 (288)15/15
P-zero tran noiseless 9.4 (8)44 (25)111 (42)111 (52)111 (39)116 (240)223 (66)15/15
PRCGA sawyerr noiseless 1.3 (0.5)7.1 (4)17 (19)19 (29)19 (19)23 (15)26 (44)15/15
SMAC-BBOB hutter noiseless 5.1 (5)5000/15
U-DCN tran noiseless 0.85 (0.5)3.6 (2)5.4 (2)8.1 (4)10 (4)65 (64)374 (672)13/15
U-zero tran noiseless 0.62 (0.4)2.4 (1)8.4 (7)35 (36)88 (40)1027 (1066)5e60/15
fmincon pal noiseless 5.2 (4)122 (155)6e40/15
fminunc pal noiseless 5.3 (4)253 (323)6e40/15
lmm-CMA-ES auger noiseless 0.45 (0.7)5.3 (11)28060/15
simplex pal noiseless 12 (7)698 (680)692 (954)690 (988)688 (961)686 (1022)685 (1144)1/15
tany liao noiseless 0.94 (0.8)7.2 (3)51 (29)51 (74)51 (31)51 (31)52 (78)15/15
texp liao noiseless 1.1 (0.1)10 (11)42 (107)43 (25)43 (32)43 (12)44 (64)15/15

Δ fopt
f4, 5-D
1e1
809
1e0
1633
1e-1
1688
1e-2
1758
1e-3
1817
1e-5
1886
1e-7
1903
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.26 (0.1)0.60 (0.3)0.85 (0.1)1.1 (0.2)1.3 (0.3)1.6 (0.2)1.9 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1.7 (2)9029 (9510)5e60/15
CGA-grid100 holtschulte noiseless 7.2 (4)24 (9)58 (41)708 (924)2e50/15
CGA-grid16 holtschulte noiseless 1.6 (0.5)5.4 (3)17 (8)44 (32)302 (322)2e50/15
CGA-ring100 holtschulte noiseless 5.0 (0.8)10 (1)19 (5)34 (18)86 (95)2e50/15
CGA-ring16 holtschulte noiseless 1.1 (0.4)2.7 (0.7)7.0 (3)19 (9)66 (48)2e50/15
CMAES Hutter hutter noiseless 1.1 (0.8)5060/15
DE Pal pal noiseless 1.3 (0.6)12 (31)165 (207)159 (86)154 (151)149 (265)148 (118)4/15
GA-100 holtschulte noiseless 2.5 (0.7)5.9 (3)15 (4)34 (15)182 (193)2e50/15
HCMA loshchilov noiseless 0.29 (0.1)74 (526)457 (741)439 (712)425 (0.3)410 (0.3)406 (1315)13/15
HILL holtschulte noiseless 0.48 (0.1)2.1 (1)7.8 (4)27 (19)88 (44)2e50/15
HMLSL pal noiseless 1.5 (0.7)13 (1)93 (163)90 (142)87 (111)84 (94)83 (92)6/15
IP-10DDr liao noiseless 2.6 (0.8)2722 (2493)4.3e4 (3e4)4.1e4 (3e4)4.0e4 (3e4)3.8e4 (2e4)3.8e4 (4e4)1/15
IP-500 liao noiseless 2.6 (3)5e60/15
IPOP400D auger noiseless 1.5 (0.2)28050/15
IP liao noiseless 2.6 (2)5e60/15
MEMPSODE voglis noiseless 3.2 (3)12 (4)23 (9)25 (4)24 (19)23 (23)24 (22)15/15
MLSL pal noiseless 22 (24)6e40/15
OQNLP pal noiseless 25 (25)2e40/15
P-DCN tran noiseless 42 (43)74 (91)210 (317)201 (188)195 (273)189 (71)189 (258)15/15
P-zero tran noiseless 24 (8)81 (125)139 (142)134 (186)131 (34)132 (34)256 (67)15/15
PRCGA sawyerr noiseless 2.0 (1)11 (6)32 (31)33 (31)34 (22)46 (42)55 (61)15/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 1.1 (0.6)6.1 (3)8.2 (4)10 (6)12 (5)89 (193)876 (1496)8/15
U-zero tran noiseless 0.76 (0.3)4.7 (4)12 (11)31 (35)112 (72)1134 (497)5e60/15
fmincon pal noiseless 12 (11)7e40/15
fminunc pal noiseless 27 (44)6e40/15
lmm-CMA-ES auger noiseless 1.1 (0.5)28100/15
simplex pal noiseless 40 (38)8e40/15
tany liao noiseless 2.0 (3)3010 (3758)5e60/15
texp liao noiseless 1.6 (2)5051 (3585)5e60/15

Δ fopt
f5, 5-D
1e1
10
1e0
10
1e-1
10
1e-2
10
1e-3
10
1e-5
10
1e-7
10
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.2 (0)1.2 (0)1.2 (0)1.2 (0)1.2 (0)1.2 (0)1.2 (0)15/15
BIPOP-saACM-k loshchilov noiseless 4.9 (1)6.3 (3)6.4 (2)6.4 (2)6.4 (2)6.4 (2)6.4 (3)15/15
CGA-grid100 holtschulte noiseless 116 (60)247 (123)264 (54)264 (108)264 (113)264 (84)264 (115)15/15
CGA-grid16 holtschulte noiseless 28 (8)46 (15)49 (13)50 (13)51 (15)51 (11)51 (12)15/15
CGA-ring100 holtschulte noiseless 94 (32)171 (29)190 (42)201 (29)201 (37)201 (51)201 (33)15/15
CGA-ring16 holtschulte noiseless 20 (4)41 (16)47 (20)47 (10)48 (12)48 (13)48 (14)15/15
CMAES Hutter hutter noiseless 4.0 (2)5.5 (1)5.6 (0.9)5.6 (1)5.6 (3)5.6 (1)5.6 (1)15/15
DE Pal pal noiseless 29 (13)108 (9)193 (33)295 (33)389 (29)572 (54)771 (41)15/15
GA-100 holtschulte noiseless 55 (19)100 (31)121 (27)124 (22)124 (18)124 (31)124 (27)15/15
HCMA loshchilov noiseless 1.3 (0.1)1.4 (0.2)1.5 (0.1)1.5 (0.3)1.5 (0.2)1.5 (0.2)1.5 (0.3)15/15
HILL holtschulte noiseless 7.6 (3)11 (5)11 (5)11 (3)11 (4)11 (4)11 (5)15/15
HMLSL pal noiseless 2.5 (0)4.3 (0)5.5 (0)5.5 (0)6.1 (0)6.7 (0)87 (119)15/15
IP-10DDr liao noiseless 6.2 (6)23 (13)30 (19)34 (28)41 (30)45 (48)46 (21)15/15
IP-500 liao noiseless 6.2 (6)23 (21)30 (19)34 (27)41 (26)45 (24)46 (33)15/15
IPOP400D auger noiseless 4.0 (1)5.9 (4)6.2 (3)6.2 (2)6.2 (3)6.2 (3)6.2 (2)15/15
IP liao noiseless 6.2 (2)23 (19)30 (23)34 (33)41 (28)45 (44)46 (42)15/15
MEMPSODE voglis noiseless 10 (6)14 (3)14 (2)14 (6)14 (5)14 (7)14 (3)15/15
MLSL pal noiseless 2.5 (0)4.3 (0)5.5 (0)5.5 (0)6.1 (0)6.7 (0)18 (19)14/15
OQNLP pal noiseless 2.3 (0)2.4 (0)2.4 (0)2.4 (0)2.4 (0)2.4 (0)2.4 (0)15/15
P-DCN tran noiseless 37 (31)118 (71)132 (53)145 (30)168 (25)219 (13)290 (76)15/15
P-zero tran noiseless 50 (65)101 (90)113 (80)120 (74)129 (78)146 (75)162 (74)15/15
PRCGA sawyerr noiseless 318 (249)1999 (2885)4233 (3837)1.1e4 (7374)7.0e4 (7e4)3e50/15
SMAC-BBOB hutter noiseless 0.88 (0.1)★40.91 (0.1)★40.95 (0.1)★30.95 (0.1)★30.95 (0.1)★30.95 (0.1)★30.95 (0.1)★315/15
U-DCN tran noiseless 25 (13)240 (156)988 (261)1733 (943)3.7e4 (1e5)2.6e5 (5e5)1.5e6 (3e6)2/15
U-zero tran noiseless 19 (18)217 (81)2697 (1521)3.6e4 (1e4)2.5e5 (6e4)5e60/15
fmincon pal noiseless 2.5 (0)4.3 (0)5.5 (0)5.5 (0)6.1 (0)6.7 (0)25 (22)13/15
fminunc pal noiseless 1.9 (0)2.5 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)15/15
lmm-CMA-ES auger noiseless 3.4 (1)4.8 (0.8)5.0 (0.7)5.0 (1)5.0 (1)5.0 (2)5.0 (1)15/15
simplex pal noiseless 74 (117)89 (93)90 (160)90 (69)90 (76)90 (129)90 (94)15/15
tany liao noiseless 8.6 (7)32 (26)40 (19)47 (27)54 (28)62 (66)65 (45)15/15
texp liao noiseless 12 (12)36 (42)49 (51)58 (64)67 (76)76 (46)88 (53)15/15

Δ fopt
f6, 5-D
1e1
114
1e0
214
1e-1
281
1e-2
404
1e-3
580
1e-5
1038
1e-7
1332
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.4 (0.7)2.1 (0.5)2.2 (0.4)1.9 (0.4)1.6 (0.2)1.2 (0.3)1.2 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 2.4 (3)2.2 (0.8)2.5 (1)2.3 (1)1.9 (0.4)1.4 (0.5)1.5 (0.5)15/15
CGA-grid100 holtschulte noiseless 29 (16)252 (113)964 (549)2e50/15
CGA-grid16 holtschulte noiseless 8.3 (5)47 (24)400 (444)780 (1085)2957 (3766)2e50/15
CGA-ring100 holtschulte noiseless 17 (6)53 (18)136 (57)284 (117)1527 (1340)2e50/15
CGA-ring16 holtschulte noiseless 4.7 (3)11 (6)46 (44)386 (411)682 (1037)2e50/15
CMAES Hutter hutter noiseless 1.9 (0.5)1.9 (0.4)4.3 (3)5060/15
DE Pal pal noiseless 2.5 (1.0)5.1 (2)7.6 (2)8.6 (1)8.9 (2)8.1 (2)8.9 (2)15/15
GA-100 holtschulte noiseless 11 (4)31 (14)104 (101)951 (1219)3096 (3402)2e50/15
HCMA loshchilov noiseless 2.5 (2)2.3 (0.7)2.9 (2)2.5 (2)2.0 (0.3)1.5 (0.9)1.4 (0.7)15/15
HILL holtschulte noiseless 2.8 (1)13 (14)192 (101)483 (363)832 (916)2e50/15
HMLSL pal noiseless 1.2 (0.6)1.1 (0.5)1.2 (0.4)1.0 (0.2)0.85 (0.3)0.73 (0.2)0.71 (0.3)15/15
IP-10DDr liao noiseless 1.6 (1)1.8 (0.4)2.1 (0.2)1.9 (0.2)1.6 (0.2)1.2 (0.1)1.2 (0.1)15/15
IP-500 liao noiseless 1.6 (0.6)1.8 (0.3)2.1 (0.3)1.9 (0.3)1.6 (0.2)1.2 (0.1)1.2 (0.1)15/15
IPOP400D auger noiseless 2.2 (0.6)2.3 (0.8)2.3 (0.3)2.0 (0.3)1.7 (0.4)1.3 (0.1)1.3 (0.2)15/15
IP liao noiseless 1.6 (0.4)1.8 (0.4)2.1 (0.3)1.9 (0.3)1.6 (0.2)1.2 (0.1)1.2 (0.1)15/15
MEMPSODE voglis noiseless 3.3 (2)2.9 (3)2.8 (2)2.3 (1)1.8 (0.9)2.2 (1.0)3.7 (6)15/15
MLSL pal noiseless 1.2 (0.5)1.1 (0.6)1.2 (0.3)1.0 (0.4)0.85 (0.3)0.73 (0.2)0.71 (0.2)15/15
OQNLP pal noiseless 0.98 (0.8)0.99 (0.5)1.00 (0.3)1.3 (1)2.3 (4)7.3 (13)20 (11)2/15
P-DCN tran noiseless 7.6 (7)7.6 (2)8.3 (5)13 (5)23 (17)74 (92)410 (991)14/15
P-zero tran noiseless 7.3 (6)6.4 (4)8.8 (7)12 (11)109 (499)1887 (2385)6887 (1e4)4/15
PRCGA sawyerr noiseless 7.1 (5)202 (197)243 (395)327 (425)410 (480)362 (412)337 (442)10/15
SMAC-BBOB hutter noiseless 5.2 (5)5000/15
U-DCN tran noiseless 7.7 (3)96 (15)293 (613)1254 (303)2098 (1339)3874 (8617)5.3e4 (3e4)1/15
U-zero tran noiseless 6.5 (15)77 (148)1679 (1048)4706 (9452)8128 (3e4)9428 (1e4)5e60/15
fmincon pal noiseless 1.2 (0.5)1.1 (0.4)1.2 (0.5)1.0 (0.4)0.85 (0.3)0.67 (0.2)0.68 (0.1)15/15
fminunc pal noiseless 1.8 (1)2.2 (1)2.6 (0.7)2.5 (0.8)2.1 (0.5)1.8 (0.8)6.4 (4)14/15
lmm-CMA-ES auger noiseless 4.0 (6)4.3 (4)4.5 (3)3.9 (2)4.8 (2)5.4 (6)28040/15
simplex pal noiseless 15 (6)13 (4)13 (6)12 (10)16 (17)20 (23)43 (12)7/15
tany liao noiseless 1.5 (0.6)1.9 (0.6)2.1 (0.4)1.9 (0.2)1.6 (0.2)1.3 (0.1)1.3 (0.1)15/15
texp liao noiseless 1.7 (0.8)2.0 (0.6)2.2 (0.5)2.0 (0.4)1.7 (0.3)1.3 (0.2)1.3 (0.2)15/15

Δ fopt
f7, 5-D
1e1
24
1e0
324
1e-1
1171
1e-2
1451
1e-3
1572
1e-5
1572
1e-7
1597
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 6.2 (3)1.5 (2)1.0 (0.9)0.91 (0.7)0.95 (0.6)0.95 (0.8)0.97 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 3.6 (1)1.2 (2)0.80 (0.7)0.75 (0.4)0.72 (0.3)0.72 (0.5)0.90 (0.8)15/15
CGA-grid100 holtschulte noiseless 39 (36)74 (86)266 (248)1184 (1077)2287 (1034)2287 (4890)2252 (2348)1/15
CGA-grid16 holtschulte noiseless 13 (9)97 (72)401 (732)2515 (2111)2321 (3220)2321 (1551)2299 (7671)1/15
CGA-ring100 holtschulte noiseless 27 (29)19 (12)42 (44)173 (209)319 (560)319 (186)322 (327)5/15
CGA-ring16 holtschulte noiseless 13 (12)104 (16)436 (427)717 (1077)1075 (1312)1075 (1272)1059 (898)2/15
CMAES Hutter hutter noiseless 4.1 (3)1.6 (1)0.92 (1)0.99 (0.6)0.92 (1.0)0.92 (0.4)1.5 (0.7)2/15
DE Pal pal noiseless 8.9 (6)2.8 (0.8)1.7 (0.4)2.7 (0.9)2.8 (0.8)2.8 (0.9)3.0 (1)15/15
GA-100 holtschulte noiseless 21 (10)11 (15)58 (59)131 (311)271 (304)271 (626)269 (508)6/15
HCMA loshchilov noiseless 3.4 (4)1.0 (0.9)0.68 (0.3)0.79 (0.8)0.82 (0.5)0.82 (0.6)0.85 (0.4)15/15
HILL holtschulte noiseless 20 (17)117 (217)300 (294)1227 (687)2331 (2545)2331 (795)2294 (2583)1/15
HMLSL pal noiseless 15 (3)3.8 (2)8.7 (1)8.8 (70)8.5 (18)8.5 (2)8.8 (2)14/15
IP-10DDr liao noiseless 5.2 (2)1.1 (0.9)1.2 (0.8)1.1 (0.7)1.2 (0.7)1.2 (0.7)1.3 (0.9)15/15
IP-500 liao noiseless 5.2 (2)1.1 (1)1.2 (0.6)1.1 (1.0)1.2 (0.7)1.2 (0.6)1.3 (0.9)15/15
IPOP400D auger noiseless 4.1 (3)1.3 (1)0.98 (0.7)0.91 (0.4)0.87 (0.5)0.87 (0.3)0.88 (0.4)15/15
IP liao noiseless 5.2 (3)1.1 (0.4)1.2 (0.9)1.1 (1.0)1.2 (1)1.2 (0.5)1.3 (0.8)15/15
MEMPSODE voglis noiseless 19 (11)7.5 (9)6.5 (2)8.5 (2)9.0 (2)9.0 (2)17 (17)15/15
MLSL pal noiseless 63 (36)1097 (665)5e40/15
OQNLP pal noiseless 26 (38)48 (63)28 (33)22890/15
P-DCN tran noiseless 111 (362)1694 (1620)1569 (4283)1271 (1945)1176 (556)1176 (2508)1157 (2665)12/15
P-zero tran noiseless 214 (258)2795 (7772)1284 (2324)1053 (2060)983 (1157)983 (1159)968 (1057)13/15
PRCGA sawyerr noiseless 9.3 (5)17 (29)22 (46)40 (14)45 (76)45 (42)46 (66)14/15
SMAC-BBOB hutter noiseless 2.3 (0.9)0.88 (0.8)3.1 (3)5000/15
U-DCN tran noiseless 20 (41)1131 (39)1422 (1322)4704 (5367)9510 (2e4)9510 (7952)9362 (8968)4/15
U-zero tran noiseless 11 (16)1486 (2670)2969 (3212)4578 (7855)6280 (1e4)6280 (9843)6187 (8156)6/15
fmincon pal noiseless 60 (72)1085 (1088)5e40/15
fminunc pal noiseless 54 (35)5e40/15
lmm-CMA-ES auger noiseless 3.3 (4)0.92 (0.5)0.94 (0.7)0.91 (0.6)0.90 (0.6)0.90 (0.5)1.2 (0.4)13/15
simplex pal noiseless 45 (16)154 (208)648 (637)5e40/15
tany liao noiseless 3.4 (2)1.7 (0.5)1.3 (1)1.2 (0.5)1.1 (0.7)1.1 (0.8)1.1 (0.8)15/15
texp liao noiseless 2.7 (2)2.1 (2)1.4 (1)1.3 (0.6)1.2 (0.4)1.2 (0.9)1.3 (0.6)15/15

Δ fopt
f8, 5-D
1e1
73
1e0
273
1e-1
336
1e-2
372
1e-3
391
1e-5
410
1e-7
422
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.3 (3)4.3 (4)4.7 (5)4.7 (3)4.8 (2)5.0 (3)5.2 (2)15/15
BIPOP-saACM-k loshchilov noiseless 2.2 (0.6)2.2 (2)2.3 (3)2.3 (2)2.3 (1)2.3 (2)2.4 (0.8)15/15
CGA-grid100 holtschulte noiseless 114 (90)1141 (1169)2e50/15
CGA-grid16 holtschulte noiseless 33 (26)632 (1606)2095 (4666)4614 (6641)2e50/15
CGA-ring100 holtschulte noiseless 58 (13)141 (705)560 (749)2201 (3038)4632 (1996)2e50/15
CGA-ring16 holtschulte noiseless 17 (6)624 (1147)3005 (2611)4429 (4032)2e50/15
CMAES Hutter hutter noiseless 3.1 (1)6.6 (4)5060/15
DE Pal pal noiseless 8.0 (2)7.6 (2)17 (3)22 (5)26 (3)36 (5)46 (7)15/15
GA-100 holtschulte noiseless 34 (16)487 (1152)4870 (5769)4450 (6048)9182 (1e4)2e50/15
HCMA loshchilov noiseless 2.3 (2)2.8 (2)2.8 (2)2.7 (1)2.7 (0.4)2.7 (0.2)2.7 (0.3)15/15
HILL holtschulte noiseless 8.6 (6)721 (919)1517 (3528)9493 (9241)2e50/15
HMLSL pal noiseless 1.0 (0.4)1.3 (2)1.2 (2)1.1 (0.2)1.1 (0.8)1.1 (0.8)1.1 (0.7)15/15
IP-10DDr liao noiseless 3.2 (1)4.3 (1)5.1 (2)5.4 (2)5.5 (2)5.8 (2)6.1 (2)15/15
IP-500 liao noiseless 3.2 (1)4.3 (4)5.1 (1)5.4 (2)5.5 (0.8)5.8 (1)6.1 (0.9)15/15
IPOP400D auger noiseless 3.0 (0.8)2.9 (0.9)3.7 (2)3.9 (0.8)4.0 (2)4.3 (0.9)4.6 (0.8)15/15
IP liao noiseless 3.2 (1)4.3 (0.9)5.1 (3)5.4 (1)5.5 (2)5.8 (2)6.1 (0.9)15/15
MEMPSODE voglis noiseless 3.0 (1)4.1 (0.4)3.6 (2)3.4 (8)3.8 (12)3.7 (11)3.8 (8)15/15
MLSL pal noiseless 1.0 (0.4)1.0 (0.6)0.99 (0.5)0.97 (0.6)0.95 (0.5)0.97 (0.4)0.96 (0.6)15/15
OQNLP pal noiseless 0.90 (0.4)0.71 (0.7)0.75 (0.7)0.76 (0.2)0.78 (0.4)0.78 (0.5)27 (33)0/15
P-DCN tran noiseless 23 (39)6802 (2e4)6653 (2e4)7687 (6731)9251 (6529)1.4e4 (6781)5e60/15
P-zero tran noiseless 18 (34)2865 (44)3234 (4154)7969 (8570)1.8e5 (3e5)1.7e5 (1e5)5e60/15
PRCGA sawyerr noiseless 11 (3)518 (632)9466 (7173)8754 (1e4)1.7e4 (7564)5e50/15
SMAC-BBOB hutter noiseless 4.6 (2)5000/15
U-DCN tran noiseless 17 (14)714 (1998)4012 (2059)1.1e4 (9663)1.9e5 (3e5)5e60/15
U-zero tran noiseless 16 (9)7826 (1e4)5e60/15
fmincon pal noiseless 1.0 (0.3)1.1 (0.3)1.0 (1)0.99 (0.5)0.97 (0.8)0.99 (0.5)0.98 (0.2)15/15
fminunc pal noiseless 1.2 (0.9)0.90 (0.4)0.87 (0.2)0.87 (0.3)0.87 (0.2)0.88 (0.2)0.88 (0.1)15/15
lmm-CMA-ES auger noiseless 1.6 (0.5)1.7 (2)1.8 (1)1.8 (0.8)1.8 (1)1.8 (1)1.8 (1)15/15
simplex pal noiseless 8.8 (3)4.9 (1)4.7 (1)4.8 (2)4.7 (2)4.6 (2)4.8 (2)15/15
tany liao noiseless 2.7 (0.8)3.7 (1)4.6 (0.9)4.9 (0.6)5.0 (1)5.3 (1.0)5.6 (1)15/15
texp liao noiseless 2.6 (0.6)4.7 (5)5.6 (2)5.8 (1)5.9 (1)6.1 (3)6.4 (5)15/15

Δ fopt
f9, 5-D
1e1
35
1e0
127
1e-1
214
1e-2
263
1e-3
300
1e-5
335
1e-7
369
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 7.0 (1)7.6 (11)6.4 (0.9)5.9 (1)5.6 (1.0)5.5 (0.8)5.4 (0.8)15/15
BIPOP-saACM-k loshchilov noiseless 4.6 (1)3.8 (4)3.0 (2)2.7 (2)2.5 (1)2.4 (0.4)2.3 (1.0)15/15
CGA-grid100 holtschulte noiseless 311 (554)1.3e4 (9541)1.7e4 (1e4)2e50/15
CGA-grid16 holtschulte noiseless 57 (51)1.3e4 (2e4)1.6e4 (3e4)2e50/15
CGA-ring100 holtschulte noiseless 136 (37)1261 (570)4949 (6163)2e50/15
CGA-ring16 holtschulte noiseless 30 (10)2428 (3198)2e50/15
CMAES Hutter hutter noiseless 6.0 (3)9.2 (7)5060/15
DE Pal pal noiseless 24 (7)24 (13)30 (5)34 (10)38 (10)49 (6)57 (18)15/15
GA-100 holtschulte noiseless 57 (20)2015 (1019)1.6e4 (3e4)2e50/15
HCMA loshchilov noiseless 5.6 (4)5.4 (6)4.0 (4)3.5 (0.4)3.2 (2)3.0 (1)2.8 (1)15/15
HILL holtschulte noiseless 13 (12)4153 (4030)2e50/15
HMLSL pal noiseless 0.93 (0.1)0.64 (0.1)0.61 (0.0)0.59 (0.1)0.57 (0.0)0.56 (0.0)0.54 (0.0)15/15
IP-10DDr liao noiseless 6.1 (3)10 (2)8.6 (9)8.0 (3)7.6 (3)7.4 (5)7.2 (3)15/15
IP-500 liao noiseless 6.1 (2)10 (2)8.6 (4)8.0 (1)7.6 (5)7.4 (6)7.2 (2)15/15
IPOP400D auger noiseless 4.9 (2)9.0 (3)7.4 (2)6.9 (1)6.4 (3)6.4 (3)6.7 (4)13/15
IP liao noiseless 6.1 (1)10 (2)8.6 (3)8.0 (6)7.6 (2)7.4 (4)7.2 (5)15/15
MEMPSODE voglis noiseless 5.8 (2)7.5 (14)4.8 (9)4.1 (7)3.8 (3)3.6 (6)3.4 (5)15/15
MLSL pal noiseless 0.93 (0.1)0.64 (0.1)0.61 (0.1)0.59 (0.1)0.57 (0.1)0.56 (0.0)0.54 (0.0)15/15
OQNLP pal noiseless 0.71 (0.0)0.51 (6e-3)0.52 (2e-3)0.55 (0.0)0.54 (0.0)0.53 (8e-3)1.3 (0.0)10/15
P-DCN tran noiseless 441 (966)2.7e4 (3e4)1.7e4 (2e4)1.7e4 (3e4)1.9e4 (2e4)5.1e4 (4e4)2.0e5 (1e5)0/15
P-zero tran noiseless 677 (1033)3145 (253)3476 (1213)3.0e4 (3e4)2.4e5 (4e5)5e60/15
PRCGA sawyerr noiseless 11 (8)957 (1151)5e50/15
SMAC-BBOB hutter noiseless 12 (5)5000/15
U-DCN tran noiseless 64 (47)3.1e4 (3e4)2.3e4 (1e4)2.9e4 (4e4)7.2e4 (1e5)5e60/15
U-zero tran noiseless 373 (35)1.4e4 (2e4)3.4e5 (5e5)5e60/15
fmincon pal noiseless 0.93 (0)0.64 (0.1)0.61 (0.1)0.59 (0.1)0.57 (0.0)0.56 (0.0)0.54 (0.0)15/15
fminunc pal noiseless 0.54 (0)★40.25 (0)★40.50 (0.0)0.51 (0.0)★30.50 (0.0)★20.49 (0.0)★30.47 (0.0)★415/15
lmm-CMA-ES auger noiseless 2.7 (1)3.4 (1.0)2.6 (1)2.4 (1)2.2 (1)2.1 (1)1.9 (0.4)15/15
simplex pal noiseless 5.0 (3)3.8 (2)3.6 (0.8)3.2 (0.8)2.9 (0.6)2.8 (0.5)2.6 (0.6)15/15
tany liao noiseless 5.2 (2)11 (13)8.7 (9)8.1 (4)7.6 (6)7.6 (1)7.4 (3)15/15
texp liao noiseless 3.0 (1)8.1 (3)7.4 (2)6.9 (4)6.6 (5)6.5 (3)6.4 (2)15/15

Δ fopt
f10, 5-D
1e1
349
1e0
500
1e-1
574
1e-2
607
1e-3
626
1e-5
829
1e-7
880
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.8 (0.4)2.2 (0.2)2.1 (0.2)2.1 (0.1)2.1 (0.1)1.8 (0.1)1.9 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 0.78 (0.1)0.61 (0.1)0.58 (0.0)0.59 (0.1)0.62 (0.1)0.53 (0.1)0.55 (0.1)15/15
CGA-grid100 holtschulte noiseless 2e50/15
CGA-grid16 holtschulte noiseless 2e50/15
CGA-ring100 holtschulte noiseless 1.0e4 (2e4)2e50/15
CGA-ring16 holtschulte noiseless 2e50/15
CMAES Hutter hutter noiseless 5060/15
DE Pal pal noiseless 23 (8)26 (5)29 (4)37 (5)42 (4)44 (3)52 (4)15/15
GA-100 holtschulte noiseless 3070 (6328)2e50/15
HCMA loshchilov noiseless 1.1 (0.1)0.81 (0.1)0.76 (0.1)0.75 (0.1)0.77 (0.1)0.64 (0.1)0.65 (0.1)15/15
HILL holtschulte noiseless 1.0e4 (1e4)2e50/15
HMLSL pal noiseless 0.28 (0.1)0.23 (0.0)0.22 (0.1)0.23 (0.1)0.60 (1)18 (51)104 (149)8/15
IP-10DDr liao noiseless 3.4 (0.8)3.1 (0.9)3.1 (0.4)3.1 (0.2)3.2 (0.3)2.6 (0.3)2.7 (0.2)15/15
IP-500 liao noiseless 3.4 (1)3.1 (0.5)3.1 (0.4)3.1 (0.4)3.2 (0.2)2.6 (0.1)2.7 (0.2)15/15
IPOP400D auger noiseless 3.6 (0.5)3.0 (0.4)2.8 (0.2)2.8 (0.2)2.8 (0.3)2.3 (0.2)2.4 (0.2)15/15
IP liao noiseless 3.4 (1)3.1 (0.6)3.1 (0.2)3.1 (0.3)3.2 (0.2)2.6 (0.3)2.7 (0.2)15/15
MEMPSODE voglis noiseless 3.7 (4)3.5 (8)3.2 (0.4)3.5 (3)4.6 (9)7.5 (10)11 (7)15/15
MLSL pal noiseless 0.28 (0.1)0.23 (0.1)0.22 (0.0)0.23 (0.1)0.60 (0.1)16 (15)129 (287)3/15
OQNLP pal noiseless 0.38 (0.2)0.41 (0.5)0.89 (1)1.5 (2)6.5 (6)120 (191)2e40/15
P-DCN tran noiseless 7429 (9159)6.6e4 (1e5)1.3e5 (2e5)1.2e5 (1e5)1.2e5 (5e4)5e60/15
P-zero tran noiseless 2.3e4 (2e4)1.4e5 (1e5)5e60/15
PRCGA sawyerr noiseless 5559 (4929)5e50/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 9.9e4 (7e4)5e60/15
U-zero tran noiseless 2.1e5 (3e5)5e60/15
fmincon pal noiseless 0.28 (0.1)0.22 (0.1)0.21 (0.0)0.21 (0.1)1.8 (6)19 (41)150 (169)2/15
fminunc pal noiseless 0.99 (0.5)1.0 (0.3)1.0 (0.2)1.1 (0.3)1.1 (0.2)2.4 (2)92 (36)5/15
lmm-CMA-ES auger noiseless 0.77 (0.3)0.67 (0.2)0.65 (0.2)0.65 (0.2)0.66 (0.1)0.54 (0.0)0.55 (0.1)15/15
simplex pal noiseless 5.5 (2)4.5 (2)4.3 (0.7)4.3 (0.9)4.3 (0.6)3.3 (0.4)3.2 (0.4)15/15
tany liao noiseless 3.4 (0.8)3.1 (0.4)2.9 (0.2)3.0 (0.4)3.0 (0.2)2.5 (0.1)2.6 (0.2)15/15
texp liao noiseless 3.4 (1)3.1 (0.4)3.1 (0.3)3.1 (0.4)3.1 (0.5)2.6 (0.2)2.6 (0.1)15/15

Δ fopt
f11, 5-D
1e1
143
1e0
202
1e-1
763
1e-2
977
1e-3
1177
1e-5
1467
1e-7
1673
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.8 (0.9)5.0 (0.5)1.4 (0.2)1.2 (0.1)1.1 (0.1)0.97 (0.0)0.94 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 2.0 (0.3)1.6 (0.2)0.46 (0.1)0.38 (0.0)0.34 (0.0)0.30 (0.0)0.29 (0.0)15/15
CGA-grid100 holtschulte noiseless 2791 (3252)2e50/15
CGA-grid16 holtschulte noiseless 750 (581)4200 (5260)2e50/15
CGA-ring100 holtschulte noiseless 188 (182)3939 (5088)4712 (2457)2e50/15
CGA-ring16 holtschulte noiseless 295 (434)1713 (1568)2e50/15
CMAES Hutter hutter noiseless 24 (16)5060/15
DE Pal pal noiseless 23 (9)36 (12)16 (5)17 (5)18 (6)20 (5)23 (4)15/15
GA-100 holtschulte noiseless 202 (93)1651 (2578)2e50/15
HCMA loshchilov noiseless 2.6 (0.2)2.0 (0.2)0.56 (0.1)0.46 (0.1)0.40 (0.0)0.35 (0.0)0.34 (0.0)15/15
HILL holtschulte noiseless 196 (171)844 (953)4822 (2867)2e50/15
HMLSL pal noiseless 0.24 (0.1)0.21 (0.0)0.07 (0.0)0.07 (0.0)1.0 (3)76 (133)441 (243)2/15
IP-10DDr liao noiseless 7.3 (4)7.1 (1)2.1 (0.2)1.8 (0.3)1.6 (0.1)1.4 (0.1)1.3 (0.1)15/15
IP-500 liao noiseless 7.3 (4)7.1 (0.7)2.1 (0.2)1.8 (0.1)1.6 (0.1)1.4 (0.1)1.3 (0.1)15/15
IPOP400D auger noiseless 7.8 (1)7.0 (1.0)2.1 (0.3)1.8 (0.2)1.5 (0.2)1.4 (0.1)1.3 (0.1)15/15
IP liao noiseless 7.3 (3)7.1 (1)2.1 (0.3)1.8 (0.1)1.6 (0.1)1.4 (0.1)1.3 (0.1)15/15
MEMPSODE voglis noiseless 1.4 (0.1)7.0 (11)3.5 (3)3.7 (2)3.4 (2)4.0 (0.6)5.4 (5)15/15
MLSL pal noiseless 0.24 (0.0)0.21 (0.0)0.07 (0.0)0.07 (0.0)1.4 (1)56 (37)868 (864)0/15
OQNLP pal noiseless 0.41 (0.1)0.94 (3)0.53 (0.6)2.1 (3)4.7 (2)142 (48)3e40/15
P-DCN tran noiseless 605 (483)895 (570)312 (191)318 (183)619 (327)1.2e4 (1e4)5e60/15
P-zero tran noiseless 779 (507)1262 (890)479 (259)474 (168)797 (180)5.1e4 (8e4)5e60/15
PRCGA sawyerr noiseless 1327 (896)3e50/15
SMAC-BBOB hutter noiseless 15 (25)5000/15
U-DCN tran noiseless 239 (422)2583 (2252)8585 (2e4)5e60/15
U-zero tran noiseless 446 (310)2843 (4152)9231 (6126)5e60/15
fmincon pal noiseless 0.24 (0.1)0.22 (0.1)0.07 (0.0)0.07 (0.0)1.1 (4)59 (65)1e50/15
fminunc pal noiseless 0.90 (0.4)1.7 (3)1.5 (1)2.8 (6)19 (44)288 (272)1e50/15
lmm-CMA-ES auger noiseless 1.9 (0.6)1.8 (0.5)0.54 (0.1)0.45 (0.1)0.38 (0.1)0.34 (0.0)0.32 (0.0)15/15
simplex pal noiseless 8.5 (9)11 (5)4.0 (1.0)3.1 (0.7)2.8 (1)2.3 (1)2.1 (1)15/15
tany liao noiseless 8.0 (1)7.1 (0.9)2.1 (0.2)1.8 (0.1)1.5 (0.1)1.4 (0.1)1.3 (0.1)15/15
texp liao noiseless 6.8 (3)6.7 (1)2.0 (0.2)1.7 (0.2)1.5 (0.2)1.3 (0.1)1.3 (0.1)15/15

Δ fopt
f12, 5-D
1e1
108
1e0
268
1e-1
371
1e-2
413
1e-3
461
1e-5
1303
1e-7
1494
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 7.0 (3)4.7 (3)5.0 (2)5.1 (2)5.1 (3)2.3 (1)2.3 (1)15/15
BIPOP-saACM-k loshchilov noiseless 3.0 (0.4)1.9 (3)2.2 (4)2.3 (2)2.4 (2)1.2 (0.8)1.3 (0.9)15/15
CGA-grid100 holtschulte noiseless 3819 (1948)2e50/15
CGA-grid16 holtschulte noiseless 836 (704)6618 (1e4)2e50/15
CGA-ring100 holtschulte noiseless 1020 (497)1997 (3059)2e50/15
CGA-ring16 holtschulte noiseless 604 (1200)1171 (1444)4717 (6847)2e50/15
CMAES Hutter hutter noiseless 17 (7)28 (23)5060/15
DE Pal pal noiseless 61 (22)50 (41)70 (26)84 (64)94 (64)58 (45)64 (36)11/15
GA-100 holtschulte noiseless 1061 (855)2351 (3322)9846 (1e4)2e50/15
HCMA loshchilov noiseless 4.7 (7)4.4 (0.5)5.9 (17)5.7 (21)5.9 (12)6.1 (20)5.7 (0.2)15/15
HILL holtschulte noiseless 4978 (4759)6170 (5136)9644 (1e4)2e50/15
HMLSL pal noiseless 1.3 (0.4)0.94 (0.2)0.89 (0.6)0.91 (0.7)0.93 (0.6)3.3 (9)30 (38)8/15
IP-10DDr liao noiseless 7.9 (5)5.9 (4)6.0 (1.0)6.2 (3)6.3 (4)2.8 (2)2.8 (2)15/15
IP-500 liao noiseless 7.9 (5)5.9 (3)6.0 (2)6.2 (3)6.3 (1)2.8 (2)2.8 (1)15/15
IPOP400D auger noiseless 9.4 (13)9.3 (8)12 (10)12 (14)20 (17)7.5 (6)8.9 (10)3/15
IP liao noiseless 7.9 (6)5.9 (5)6.0 (5)6.2 (3)6.3 (1)2.8 (2)2.8 (2)15/15
MEMPSODE voglis noiseless 7.5 (12)4.8 (3)5.2 (4)5.3 (5)5.0 (7)7.7 (17)11 (21)15/15
MLSL pal noiseless 1.3 (0.4)0.94 (0.6)0.89 (0.6)0.91 (0.6)0.93 (0.6)1.5 (2)38 (41)5/15
OQNLP pal noiseless 1.2 (0.7)0.95 (0.7)1.2 (1)2.3 (2)20 (2)21 (26)328 (151)0/15
P-DCN tran noiseless 1.2e4 (2e4)2.8e4 (5e4)1.9e5 (2e5)5e60/15
P-zero tran noiseless 9.3e4 (2e5)1.2e5 (2e5)8.8e4 (1e5)5e60/15
PRCGA sawyerr noiseless 214 (748)296 (190)1402 (1196)2982 (2317)4284 (8505)3e50/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 1.7e4 (1e4)3.7e4 (4e4)8.8e4 (1e5)5e60/15
U-zero tran noiseless 2.4e4 (5e4)3.8e4 (3e4)8.9e4 (1e5)5e60/15
fmincon pal noiseless 1.3 (0.4)0.94 (0.7)0.90 (0.5)0.91 (0.6)0.93 (0.7)1.0 (0.8)29 (14)5/15
fminunc pal noiseless 1.0 (1)1.1 (1)1.2 (1)1.2 (0.8)1.5 (2)2.4 (4)80 (67)3/15
lmm-CMA-ES auger noiseless 1.5 (0.9)1.3 (1)1.4 (2)1.6 (2)1.7 (2)0.92 (2)0.95 (0.6)13/15
simplex pal noiseless 11 (5)6.6 (3)8.3 (3)7.9 (2)8.7 (10)4.6 (6)4.2 (7)15/15
tany liao noiseless 6.2 (0.6)7.1 (5)7.5 (4)8.2 (6)8.2 (5)3.7 (2)3.7 (1)15/15
texp liao noiseless 11 (5)8.7 (7)8.3 (7)8.6 (5)8.5 (7)3.7 (2)3.7 (3)15/15

Δ fopt
f13, 5-D
1e1
132
1e0
195
1e-1
250
1e-2
319
1e-3
1310
1e-5
1752
1e-7
2255
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.4 (1)3.9 (1)4.2 (0.9)3.9 (0.6)1.1 (0.2)1.1 (0.2)1.1 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1.4 (0.5)1.3 (0.4)1.3 (0.3)1.2 (0.2)0.36 (0.1)0.37 (0.1)0.34 (0.0)15/15
CGA-grid100 holtschulte noiseless 8040 (8523)9286 (8333)2e50/15
CGA-grid16 holtschulte noiseless 1006 (491)1.8e4 (1e4)2e50/15
CGA-ring100 holtschulte noiseless 152 (63)755 (553)2e50/15
CGA-ring16 holtschulte noiseless 730 (2366)5302 (4912)2e50/15
CMAES Hutter hutter noiseless 3.4 (1)13 (14)5060/15
DE Pal pal noiseless 11 (3)23 (9)43 (14)57 (12)20 (6)26 (4)28 (2)15/15
GA-100 holtschulte noiseless 1722 (2373)8935 (4167)2e50/15
HCMA loshchilov noiseless 1.6 (1)1.6 (0.3)1.6 (0.3)1.6 (0.5)0.45 (0.1)0.42 (0.1)0.38 (0.1)15/15
HILL holtschulte noiseless 2193 (3822)5703 (3707)2e50/15
HMLSL pal noiseless 0.74 (0.1)0.76 (0.1)0.80 (0.1)0.78 (0.0)2.0 (4)21 (22)164 (110)0/15
IP-10DDr liao noiseless 4.7 (6)5.8 (3)5.7 (3)5.3 (2)1.6 (0.5)1.9 (0.4)1.9 (0.5)15/15
IP-500 liao noiseless 4.7 (3)5.8 (4)5.7 (2)5.3 (2)1.6 (0.5)1.9 (0.5)1.9 (0.8)15/15
IPOP400D auger noiseless 3.4 (1)4.6 (2)4.8 (1)5.3 (2)1.4 (0.4)2.0 (0.9)18 (27)1/15
IP liao noiseless 4.7 (0.9)5.8 (3)5.7 (3)5.3 (2)1.6 (0.8)1.9 (0.8)1.9 (0.3)15/15
MEMPSODE voglis noiseless 3.8 (0.1)3.0 (5)2.5 (7)2.1 (3)2.9 (1.0)2.6 (0.4)2.1 (0.3)15/15
MLSL pal noiseless 0.74 (0.1)0.76 (0.0)0.80 (0.0)0.78 (0.0)4.2 (13)50 (53)7e40/15
OQNLP pal noiseless 0.95 (0.3)0.89 (0.3)0.83 (0.3)3.1 (4)8.4 (11)3e40/15
P-DCN tran noiseless 3.4e4 (4e4)3.6e5 (3e5)2.8e5 (4e5)5e60/15
P-zero tran noiseless 7.6e4 (7e4)1.7e5 (1e5)2.8e5 (2e5)5e60/15
PRCGA sawyerr noiseless 118 (412)695 (1310)2367 (1824)2345 (1912)1743 (1021)3e50/15
SMAC-BBOB hutter noiseless 4.2 (2)5000/15
U-DCN tran noiseless 1.4e4 (2e4)5.1e4 (6e4)2.8e5 (2e5)5e60/15
U-zero tran noiseless 2.5e4 (5e4)1.7e5 (2e5)2.8e5 (4e5)2.3e5 (3e5)5e60/15
fmincon pal noiseless 0.74 (0.1)0.76 (0.0)0.80 (0.1)0.77 (0.0)4.1 (0.0)61 (77)7e40/15
fminunc pal noiseless 0.93 (0.2)1.00 (0.2)0.98 (0.1)0.96 (0.1)4.9 (4)167 (208)7e40/15
lmm-CMA-ES auger noiseless 1.3 (0.3)1.8 (0.7)1.7 (0.5)1.8 (0.6)0.50 (0.2)0.49 (0.1)0.57 (0.1)14/15
simplex pal noiseless 16 (9)17 (11)17 (12)19 (13)5.0 (4)5.1 (1)10 (16)13/15
tany liao noiseless 3.9 (3)5.5 (3)5.9 (2)5.9 (2)1.6 (0.4)1.7 (0.2)1.7 (0.3)15/15
texp liao noiseless 3.7 (1)5.4 (2)6.5 (2)5.9 (1)1.6 (0.2)1.7 (0.4)1.7 (0.2)15/15

Δ fopt
f14, 5-D
1e1
10
1e0
41
1e-1
58
1e-2
90
1e-3
139
1e-5
251
1e-7
476
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.9 (3)3.4 (1)4.4 (1)4.3 (0.8)4.3 (0.8)4.3 (0.6)3.3 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 1.4 (1)2.5 (0.5)3.0 (0.8)2.6 (0.6)2.1 (0.5)1.8 (0.2)1.3 (0.1)15/15
CGA-grid100 holtschulte noiseless 1.9 (3)54 (33)117 (60)685 (1450)2e50/15
CGA-grid16 holtschulte noiseless 0.79 (2)12 (7)24 (11)455 (696)2e50/15
CGA-ring100 holtschulte noiseless 1.7 (0.8)27 (12)72 (29)156 (43)2269 (3628)2e50/15
CGA-ring16 holtschulte noiseless 1.7 (3)8.3 (2)16 (6)117 (263)2.7e4 (3e4)2e50/15
CMAES Hutter hutter noiseless 1.6 (2)2.3 (1)3.9 (0.9)3.8 (0.7)10 (11)5060/15
DE Pal pal noiseless 2.1 (1)6.2 (2)11 (2)12 (2)16 (3)36 (8)46 (11)15/15
GA-100 holtschulte noiseless 1.6 (1)14 (4)37 (11)71 (30)3511 (6114)2e50/15
HCMA loshchilov noiseless 1.6 (0.6)1.5 (0.7)2.6 (2)3.4 (0.5)2.7 (0.4)2.2 (0.3)1.5 (0.2)15/15
HILL holtschulte noiseless 1.9 (2)2.2 (1)7.3 (3)218 (344)2.5e4 (3e4)2e50/15
HMLSL pal noiseless 0.67 (0.6)0.53 (0.2)0.64 (0.2)0.65 (0.1)0.67 (0.2)0.72 (0.1)72 (35)15/15
IP-10DDr liao noiseless 1.2 (2)2.4 (1)3.7 (0.9)4.1 (0.7)4.7 (1)5.7 (1)4.6 (0.2)15/15
IP-500 liao noiseless 1.2 (2)2.4 (2)3.7 (1)4.1 (0.8)4.7 (1)5.7 (0.7)4.6 (0.4)15/15
IPOP400D auger noiseless 1.0 (0.9)1.8 (0.4)3.4 (0.7)3.6 (0.7)4.3 (0.6)4.9 (0.9)4.1 (0.2)15/15
IP liao noiseless 1.2 (1)2.4 (2)3.7 (1)4.1 (0.6)4.7 (0.8)5.7 (0.6)4.6 (0.4)15/15
MEMPSODE voglis noiseless 2.6 (2)2.9 (0.4)2.4 (0.2)1.8 (0.2)1.4 (0.1)2.2 (0.0)23 (47)15/15
MLSL pal noiseless 0.67 (0.8)0.53 (0.2)0.64 (0.2)0.65 (0.2)0.67 (0.1)0.72 (0.1)792 (1120)0/15
OQNLP pal noiseless 1.3 (0.9)0.94 (0.3)1.0 (0.3)0.95 (0.2)0.80 (0.2)7.0 (7)2e40/15
P-DCN tran noiseless 2.0 (2)9.2 (4)10 (3)10 (5)112 (186)5.4e4 (7e4)5e60/15
P-zero tran noiseless 3.1 (3)11 (7)11 (4)11 (3)80 (39)5e60/15
PRCGA sawyerr noiseless 1.1 (0.9)6.7 (3)15 (2)52 (299)578 (1388)6784 (9374)3e50/15
SMAC-BBOB hutter noiseless 0.61 (0.3)2.6 (2)11 (4)5000/15
U-DCN tran noiseless 1.2 (0.7)6.8 (5)23 (15)92 (93)1264 (1760)5e60/15
U-zero tran noiseless 1.5 (2)3.6 (3)11 (6)766 (710)2.6e5 (2e5)5e60/15
fmincon pal noiseless 0.67 (0.6)0.53 (0.1)0.64 (0.2)0.65 (0.0)0.67 (0.2)0.72 (0.1)797 (770)0/15
fminunc pal noiseless 0.70 (0.6)0.84 (0.6)1.1 (0.4)1.0 (0.3)0.88 (0.2)0.84 (0.2)1710 (2161)0/15
lmm-CMA-ES auger noiseless 0.61 (0.7)1.5 (0.9)1.6 (0.5)1.8 (0.7)1.9 (0.4)1.8 (0.2)1.4 (0.1)15/15
simplex pal noiseless 6.3 (4)15 (12)17 (7)12 (3)8.9 (4)5.6 (2)3.8 (1)15/15
tany liao noiseless 0.92 (0.8)2.6 (2)3.9 (2)4.3 (0.6)4.5 (0.9)5.5 (0.7)4.2 (0.7)15/15
texp liao noiseless 0.91 (1.0)1.9 (0.9)3.0 (0.2)3.7 (0.7)3.8 (0.6)4.9 (0.6)4.0 (0.4)15/15

Δ fopt
f15, 5-D
1e1
511
1e0
9310
1e-1
19369
1e-2
19743
1e-3
20073
1e-5
20769
1e-7
21359
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 1.6 (2)0.88 (0.9)1.1 (0.7)1.1 (0.7)1.1 (0.7)1.1 (0.6)1.1 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 1.6 (0.3)0.97 (0.8)0.98 (0.6)0.97 (0.6)0.96 (0.6)0.94 (0.8)0.93 (0.4)15/15
CGA-grid100 holtschulte noiseless 334 (325)2e50/15
CGA-grid16 holtschulte noiseless 131 (254)2e50/15
CGA-ring100 holtschulte noiseless 19 (7)198 (363)2e50/15
CGA-ring16 holtschulte noiseless 44 (5)383 (712)2e50/15
CMAES Hutter hutter noiseless 1.9 (1)5060/15
DE Pal pal noiseless 4.5 (3)6.5 (3)5.9 (3)7.9 (12)7.9 (13)7.7 (7)7.5 (7)8/15
GA-100 holtschulte noiseless 9.2 (5)122 (157)2e50/15
HCMA loshchilov noiseless 1.7 (0.7)0.96 (0.8)0.96 (0.7)0.95 (0.6)0.94 (0.5)0.92 (0.6)0.90 (0.5)15/15
HILL holtschulte noiseless 142 (140)2e50/15
HMLSL pal noiseless 2.3 (0.2)5.5 (6)10 (17)10 (6)10 (15)10 (8)10 (14)6/15
IP-10DDr liao noiseless 1.5 (2)1.1 (0.6)0.85 (0.5)0.85 (0.4)0.85 (0.4)0.85 (0.3)0.86 (0.4)15/15
IP-500 liao noiseless 1.5 (0.5)1.1 (0.7)0.86 (0.7)0.86 (0.4)0.86 (0.4)0.87 (0.5)0.87 (0.4)15/15
IPOP400D auger noiseless 1.9 (1)1.1 (1)2.2 (1)28130/15
IP liao noiseless 1.5 (0.5)1.1 (0.5)0.86 (0.5)0.86 (0.5)0.86 (0.4)0.87 (0.3)0.87 (0.6)15/15
MEMPSODE voglis noiseless 14 (15)4.4 (6)5.6 (14)5.5 (4)5.4 (3)5.2 (4)5.1 (8)15/15
MLSL pal noiseless 10 (8)6e40/15
OQNLP pal noiseless 12 (5)1e40/15
P-DCN tran noiseless 6.4e4 (7e4)5e60/15
P-zero tran noiseless 4.5e4 (4e4)5e60/15
PRCGA sawyerr noiseless 23 (0.7)157 (147)3e50/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 515 (62)2163 (538)5e60/15
U-zero tran noiseless 1552 (3342)5e60/15
fmincon pal noiseless 8.2 (7)45 (82)6e40/15
fminunc pal noiseless 8.8 (7)6e40/15
lmm-CMA-ES auger noiseless 1.2 (1)1.1 (1)1.1 (0.9)2.1 (2)2.1 (4)2.0 (2)2.0 (3)1/15
simplex pal noiseless 20 (17)122 (152)8e40/15
tany liao noiseless 1.8 (0.3)0.76 (0.7)0.80 (0.3)0.80 (0.3)0.80 (0.5)0.80 (0.7)0.81 (0.6)15/15
texp liao noiseless 2.1 (2)0.94 (0.3)0.76 (0.5)0.77 (0.9)0.78 (0.9)0.79 (1)0.80 (0.3)15/15

Δ fopt
f16, 5-D
1e1
120
1e0
612
1e-1
2662
1e-2
10163
1e-3
10449
1e-5
11644
1e-7
12095
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.6 (11)3.3 (3)1.8 (2)0.67 (0.7)0.69 (0.6)0.66 (0.6)0.65 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (1)3.9 (5)2.0 (2)0.93 (0.6)0.95 (0.4)0.93 (1)0.96 (0.3)15/15
CGA-grid100 holtschulte noiseless 2.6 (4)185 (223)641 (1316)2e50/15
CGA-grid16 holtschulte noiseless 2.1 (2)98 (148)388 (820)2e50/15
CGA-ring100 holtschulte noiseless 3.1 (3)23 (24)66 (48)169 (122)2e50/15
CGA-ring16 holtschulte noiseless 1.5 (0.8)6.4 (8)117 (162)346 (320)2e50/15
CMAES Hutter hutter noiseless 2.5 (1)6.1 (6)5060/15
DE Pal pal noiseless 3.3 (3)32 (47)183 (160)1e50/15
GA-100 holtschulte noiseless 3.2 (2)75 (107)119 (211)167 (123)2e50/15
HCMA loshchilov noiseless 2.9 (1)3.6 (4)2.3 (2)0.67 (0.4)0.70 (0.9)0.66 (0.2)0.82 (0.1)15/15
HILL holtschulte noiseless 2.9 (2)373 (617)2e50/15
HMLSL pal noiseless 4.4 (2)45 (29)530 (583)1e50/15
IP-10DDr liao noiseless 2.0 (2)2.2 (3)1.1 (1)0.48 (0.5)0.58 (0.3)0.67 (0.5)0.67 (0.4)15/15
IP-500 liao noiseless 2.0 (2)2.2 (3)1.1 (2)0.48 (0.4)0.58 (0.5)0.67 (0.4)0.67 (0.6)15/15
IPOP400D auger noiseless 3.0 (10)3.1 (6)1.9 (1)28130/15
IP liao noiseless 2.0 (2)2.2 (0.2)1.1 (1)0.48 (0.4)0.58 (0.4)0.67 (0.1)0.67 (0.6)15/15
MEMPSODE voglis noiseless 3.0 (2)32 (54)28 (12)13 (10)31 (69)29 (61)95 (104)11/15
MLSL pal noiseless 4.7 (3)70 (94)9e40/15
OQNLP pal noiseless 12 (19)243 (192)118 (175)2e40/15
P-DCN tran noiseless 1.1 (2)1846 (4110)7523 (7049)3329 (2829)3290 (2034)5e60/15
P-zero tran noiseless 5.5 (17)7998 (7424)1.2e4 (2e4)6895 (6519)5e60/15
PRCGA sawyerr noiseless 3.1 (2)40 (1)46 (58)34 (50)139 (78)3e50/15
SMAC-BBOB hutter noiseless 0.42 (0.3)3.8 (3)5000/15
U-DCN tran noiseless 1.7 (0.5)90 (215)1913 (3793)3199 (3812)5e60/15
U-zero tran noiseless 1.3 (0.9)600 (1295)2031 (1510)1489 (2571)5e60/15
fmincon pal noiseless 4.1 (3)61 (42)496 (343)9e40/15
fminunc pal noiseless 12 (32)154 (220)1e50/15
lmm-CMA-ES auger noiseless 2.0 (1)2.1 (2)1.8 (3)0.70 (0.8)0.92 (1)1.1 (1)1.1 (1)3/15
simplex pal noiseless 6.3 (1)20 (25)44 (25)145 (72)1e50/15
tany liao noiseless 1.9 (0.8)2.1 (0.3)0.90 (0.6)0.54 (0.5)0.62 (0.5)0.59 (0.8)0.59 (0.8)15/15
texp liao noiseless 1.1 (1)1.5 (2)1.2 (1)0.56 (0.3)0.70 (0.8)0.68 (0.7)0.70 (0.2)15/15

Δ fopt
f17, 5-D
1e1
5.0
1e0
215
1e-1
899
1e-2
2861
1e-3
3669
1e-5
6351
1e-7
7934
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.7 (8)1.1 (0.3)1.4 (2)0.80 (0.5)0.88 (0.6)0.94 (0.4)1.0 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 5.1 (3)2.1 (0.6)1.7 (1)0.97 (0.5)1.00 (0.4)1.3 (2)1.7 (2)15/15
CGA-grid100 holtschulte noiseless 3.8 (3)29 (19)836 (1136)2e50/15
CGA-grid16 holtschulte noiseless 4.4 (8)101 (292)167 (244)595 (240)2e50/15
CGA-ring100 holtschulte noiseless 4.0 (2)16 (3)37 (15)145 (168)2e50/15
CGA-ring16 holtschulte noiseless 6.2 (7)3.7 (3)117 (171)1277 (350)2e50/15
CMAES Hutter hutter noiseless 4.2 (4)0.92 (0.5)0.73 (0.5)5060/15
DE Pal pal noiseless 5.6 (3)2.6 (2)2.3 (0.7)1.4 (0.6)1.7 (0.5)3.1 (0.7)3.2 (4)14/15
GA-100 holtschulte noiseless 3.7 (5)6.8 (2)32 (74)2e50/15
HCMA loshchilov noiseless 2.3 (0.9)1.4 (0.3)1.4 (2)0.88 (0.5)0.91 (0.5)1.5 (0.5)1.7 (1)15/15
HILL holtschulte noiseless 40 (124)411 (315)1148 (1093)2e50/15
HMLSL pal noiseless 27 (27)11 (4)8.2 (5)4.9 (2)5.3 (1)4.6 (2)6.9 (2)13/15
IP-10DDr liao noiseless 3.3 (3)0.78 (0.2)0.77 (0.1)0.48 (0.6)0.75 (0.5)1.1 (0.5)1.3 (0.4)15/15
IP-500 liao noiseless 3.3 (4)0.78 (0.3)0.77 (0.2)0.48 (0.3)0.75 (0.3)1.1 (0.5)1.3 (0.4)15/15
IPOP400D auger noiseless 2.1 (4)0.77 (0.3)0.93 (2)0.59 (0.5)0.93 (2)3.1 (2)5.2 (3)1/15
IP liao noiseless 3.3 (3)0.78 (0.2)0.77 (0.2)0.48 (0.3)0.75 (0.5)1.1 (0.5)1.3 (0.4)15/15
MEMPSODE voglis noiseless 7.2 (4)17 (22)36 (4)22 (21)27 (30)23 (20)104 (104)13/15
MLSL pal noiseless 25 (45)125 (79)1e50/15
OQNLP pal noiseless 15 (30)134 (120)2e40/15
P-DCN tran noiseless 4.5 (4)4.7e4 (5e4)7.8e4 (7e4)5e60/15
P-zero tran noiseless 5.9 (5)3.3e4 (3e4)2.3e4 (5e4)1.2e4 (2752)5e60/15
PRCGA sawyerr noiseless 2.0 (1)2.9 (2)7.2 (16)23 (38)64 (62)78 (137)77 (96)2/15
SMAC-BBOB hutter noiseless 2.6 (5)3.3 (3)5000/15
U-DCN tran noiseless 4.3 (6)6.0 (7)5088 (1e4)2.5e4 (3e4)5e60/15
U-zero tran noiseless 2.7 (2)33 (18)4878 (1e4)2.5e4 (2e4)5e60/15
fmincon pal noiseless 21 (20)171 (176)1e50/15
fminunc pal noiseless 11 (8)25 (25)6e40/15
lmm-CMA-ES auger noiseless 1.8 (0.7)0.51 (0.3)0.48 (1)0.47 (0.3)0.65 (0.2)1.2 (1)2.6 (4)1/15
simplex pal noiseless 66 (71)129 (124)8e40/15
tany liao noiseless 3.8 (5)1.1 (0.4)1.1 (1)0.74 (1.0)0.71 (1)0.83 (0.7)0.93 (0.5)15/15
texp liao noiseless 49 (329)3.0 (4)2.8 (4)1.2 (1)1.2 (0.6)1.1 (0.6)1.1 (0.3)15/15

Δ fopt
f18, 5-D
1e1
103
1e0
378
1e-1
3968
1e-2
8451
1e-3
9280
1e-5
10905
1e-7
12469
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (0.7)1.0 (0.3)0.55 (0.7)0.45 (0.3)0.70 (0.3)0.96 (0.7)0.94 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 1.4 (0.6)3.2 (5)0.77 (0.4)0.66 (0.3)0.70 (0.3)0.98 (0.8)1.0 (0.2)15/15
CGA-grid100 holtschulte noiseless 16 (6)978 (846)921 (1071)2e50/15
CGA-grid16 holtschulte noiseless 8.6 (7)461 (516)2e50/15
CGA-ring100 holtschulte noiseless 8.0 (6)32 (15)78 (123)2e50/15
CGA-ring16 holtschulte noiseless 3.6 (2)453 (666)273 (615)2e50/15
CMAES Hutter hutter noiseless 1.3 (0.6)0.93 (0.6)0.94 (0.4)5060/15
DE Pal pal noiseless 1.9 (0.7)4.9 (2)1.5 (0.5)1.6 (0.5)2.3 (0.4)4.1 (0.5)5.3 (2)13/15
GA-100 holtschulte noiseless 5.4 (4)14 (9)116 (77)2e50/15
HCMA loshchilov noiseless 1.3 (1)2.1 (5)0.74 (0.4)0.61 (0.4)0.69 (0.3)0.94 (0.4)0.96 (0.5)15/15
HILL holtschulte noiseless 36 (123)453 (383)415 (457)2e50/15
HMLSL pal noiseless 10 (8)10 (11)5.1 (8)4.2 (3)5.2 (1)6.9 (2)14 (26)5/15
IP-10DDr liao noiseless 1.1 (0.5)1.8 (0.4)0.56 (0.6)0.84 (0.5)1.0 (0.2)0.97 (0.3)1.0 (0.3)15/15
IP-500 liao noiseless 1.1 (0.2)1.8 (0.3)0.56 (0.5)0.84 (0.6)1.0 (0.2)0.97 (0.2)1.0 (0.2)15/15
IPOP400D auger noiseless 0.85 (0.5)1.4 (0.4)0.95 (1)1.4 (2)28030/15
IP liao noiseless 1.1 (0.3)1.8 (0.3)0.56 (0.5)0.84 (0.7)1.0 (0.2)0.97 (0.3)1.0 (0.2)15/15
MEMPSODE voglis noiseless 8.9 (4)30 (27)40 (87)41 (39)41 (39)44 (46)308 (200)6/15
MLSL pal noiseless 20 (48)1205 (1240)1e50/15
OQNLP pal noiseless 14 (9)190 (385)2e40/15
P-DCN tran noiseless 194 (645)2.9e4 (3e4)8440 (1e4)5e60/15
P-zero tran noiseless 938 (3012)4.0e4 (6e4)1.8e4 (5e4)5e60/15
PRCGA sawyerr noiseless 2.5 (3)3.4 (2)23 (35)48 (45)205 (129)3e50/15
SMAC-BBOB hutter noiseless 1.7 (2)19 (24)5000/15
U-DCN tran noiseless 2.5 (3)6283 (9602)8405 (1e4)5e60/15
U-zero tran noiseless 2.2 (3)7026 (3833)8805 (9960)5e60/15
fmincon pal noiseless 16 (14)959 (730)1e50/15
fminunc pal noiseless 11 (19)411 (412)7e40/15
lmm-CMA-ES auger noiseless 0.52 (0.2)0.52 (0.2)0.38 (0.2)0.43 (0.9)1.4 (1)3.8 (2)28050/15
simplex pal noiseless 25 (14)754 (668)8e40/15
tany liao noiseless 0.96 (0.3)1.8 (0.2)1.2 (2)0.76 (1)1.0 (0.3)1.1 (0.2)1.0 (1)15/15
texp liao noiseless 1.3 (0.4)2.8 (3)0.81 (0.4)0.76 (0.5)0.88 (0.6)0.90 (0.4)0.98 (0.4)15/15

Δ fopt
f19, 5-D
1e1
1
1e0
1
1e-1
242
1e-2
1.0e5
1e-3
1.2e5
1e-5
1.2e5
1e-7
1.2e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 21 (16)850 (993)139 (153)1.3 (2)1.4 (1)1.4 (0.8)1.4 (1)15/15
BIPOP-saACM-k loshchilov noiseless 20 (22)1590 (1118)76 (105)1.2 (1)1.2 (1)1.2 (1)1.2 (0.7)15/15
CGA-grid100 holtschulte noiseless 39 (37)4.8e4 (2e4)1.5e4 (2e4)2e50/15
CGA-grid16 holtschulte noiseless 50 (38)1.6e4 (2e4)4688 (4133)2e50/15
CGA-ring100 holtschulte noiseless 49 (99)6741 (5362)3412 (2882)2e50/15
CGA-ring16 holtschulte noiseless 31 (46)5321 (4077)3364 (3168)34 (44)29 (50)29 (46)2e50/15
CMAES Hutter hutter noiseless 14 (18)2283 (2556)5060/15
DE Pal pal noiseless 34 (22)3306 (1768)1087 (1291)1e50/15
GA-100 holtschulte noiseless 41 (40)3511 (3144)1122 (2044)2e50/15
HCMA loshchilov noiseless 15 (6)1195 (1033)99 (141)0.90 (1)0.80 (1.0)0.86 (0.9)0.86 (1.0)15/15
HILL holtschulte noiseless 42 (30)1.1e4 (1e4)6889 (2e4)2e50/15
HMLSL pal noiseless 1 (0)1 (0)0.17 (0.0)14 (11)13 (6)12 (15)12 (13)1/15
IP-10DDr liao noiseless 13 (22)1466 (1409)519 (404)4.0 (3)4.0 (4)4.0 (3)4.0 (2)15/15
IP-500 liao noiseless 13 (22)1466 (1228)484 (576)2.4 (1)2.4 (1)2.4 (1)2.4 (2)15/15
IPOP400D auger noiseless 1 (0)1 (0)173 (200)28050/15
IP liao noiseless 13 (12)1466 (1186)484 (465)2.3 (2)2.4 (2)2.4 (2)2.4 (2)15/15
MEMPSODE voglis noiseless 60 (122)7494 (5110)154 (172)3.1 (4)13 (13)13 (11)16 (37)10/15
MLSL pal noiseless 1 (0)1 (0)0.17 (0.0)1e50/15
OQNLP pal noiseless 1 (0)1 (0)0.10 (0)★40.30 (0.2)3.5 (5)3.6 (3)3e40/15
P-DCN tran noiseless 44 (33)5.0e5 (9e5)6.5e4 (3e4)679 (942)619 (623)618 (629)5e60/15
P-zero tran noiseless 27 (21)2.2e6 (4e6)3.1e5 (2e5)5e60/15
PRCGA sawyerr noiseless 14 (13)502 (328)55 (176)3e50/15
SMAC-BBOB hutter noiseless 1 (0)1 (0)5000/15
U-DCN tran noiseless 32 (27)1.3e4 (3e4)4.9e4 (1e4)5e60/15
U-zero tran noiseless 27 (22)7251 (5447)3.2e4 (5e4)5e60/15
fmincon pal noiseless 1 (0)1 (0)0.17 (0.0)1e50/15
fminunc pal noiseless 1 (0)1 (0)0.13 (0.0)8e40/15
lmm-CMA-ES auger noiseless 1 (0)1 (0)56 (46)28050/15
simplex pal noiseless 1 (0)1 (0)0.18 (0.0)1e50/15
tany liao noiseless 13 (16)2343 (3958)392 (270)2.8 (3)3.9 (5)3.9 (5)3.9 (5)15/15
texp liao noiseless 3.5 (3)1812 (939)746 (2161)2.9 (3)3.7 (5)3.7 (5)3.7 (4)15/15

Δ fopt
f20, 5-D
1e1
16
1e0
851
1e-1
38111
1e-2
51362
1e-3
54470
1e-5
54861
1e-7
55313
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 4.1 (2)7.6 (6)2.7 (2)2.0 (1)2.0 (1)2.0 (0.8)2.0 (1)15/15
BIPOP-saACM-k loshchilov noiseless 3.8 (3)5.5 (4)1.6 (1)1.2 (0.8)1.2 (0.3)1.2 (1.0)1.3 (1.0)15/15
CGA-grid100 holtschulte noiseless 41 (39)14 (6)14 (34)15 (13)68 (112)2e50/15
CGA-grid16 holtschulte noiseless 13 (10)8.1 (1)8.7 (6)7.1 (7)7.2 (5)2e50/15
CGA-ring100 holtschulte noiseless 32 (17)7.4 (2)1.4 (2)1.4 (3)2.1 (1)22 (27)2e50/15
CGA-ring16 holtschulte noiseless 8.5 (6)3.3 (0.5)10 (10)7.7 (6)7.7 (10)21 (22)2e50/15
CMAES Hutter hutter noiseless 4.2 (4)5060/15
DE Pal pal noiseless 7.7 (2)2.3 (1)2.4 (5)1.8 (3)1.7 (5)1.7 (3)1.7 (3)8/15
GA-100 holtschulte noiseless 18 (15)4.1 (3)10 (10)7.6 (12)7.6 (16)66 (89)2e50/15
HCMA loshchilov noiseless 0.88 (0.2)5.2 (2)1.6 (1.0)1.2 (1.0)1.1 (0.9)1.1 (0.7)1.2 (0.7)15/15
HILL holtschulte noiseless 5.7 (3)4.4 (12)18 (18)14 (22)13 (16)16 (18)2e50/15
HMLSL pal noiseless 1.4 (0)2.3 (1)4.1 (4)3.0 (7)2.9 (2)2.8 (2)2.8 (3)6/15
IP-10DDr liao noiseless 3.4 (1)12 (8)6.2 (5)4.7 (3)4.4 (4)4.4 (4)4.4 (3)15/15
IP-500 liao noiseless 3.4 (1)12 (11)2.1 (3)1.6 (1)1.5 (2)1.5 (1)1.5 (2)15/15
IPOP400D auger noiseless 2.1 (2)15 (8)28050/15
IP liao noiseless 3.4 (1)12 (9)1.7 (2)1.3 (1)1.3 (1)1.3 (0.8)1.3 (0.3)15/15
MEMPSODE voglis noiseless 5.7 (1.0)3.6 (2)5.5 (7)4.1 (4)3.9 (6)3.9 (4)4.2 (4)15/15
MLSL pal noiseless 1.4 (0)7.2 (14)21 (15)16 (37)15 (14)15 (54)15 (22)1/15
OQNLP pal noiseless 1.2 (0)5.8 (7)3.5 (3)2.6 (4)2.4 (4)2.4 (2)2.4 (1)1/15
P-DCN tran noiseless 8.6 (8)336 (7)1837 (1378)1363 (608)1285 (1010)1276 (1003)1266 (1740)1/15
P-zero tran noiseless 15 (9)371 (908)5e60/15
PRCGA sawyerr noiseless 4.9 (2)25 (48)44 (44)33 (40)31 (55)31 (34)31 (22)3/15
SMAC-BBOB hutter noiseless 0.77 (0.3)5000/15
U-DCN tran noiseless 4.5 (7)5.6 (5)367 (989)272 (294)257 (574)255 (206)261 (281)4/15
U-zero tran noiseless 4.0 (2)17 (23)527 (328)391 (780)369 (482)371 (593)390 (546)0/15
fmincon pal noiseless 1.4 (0)6.4 (7)10 (12)7.7 (11)7.3 (8)7.2 (15)7.2 (6)2/15
fminunc pal noiseless 0.81 (0)4.6 (4)6e40/15
lmm-CMA-ES auger noiseless 1.8 (1)15 (8)28140/15
simplex pal noiseless 8.3 (4)5.4 (3)27 (26)20 (24)19 (31)19 (26)19 (16)1/15
tany liao noiseless 3.0 (0.9)12 (10)5.0 (5)5.8 (4)5.5 (7)5.5 (7)5.4 (3)15/15
texp liao noiseless 1.6 (0.5)17 (12)7.1 (6)5.3 (4)5.0 (4)5.0 (4)5.0 (4)15/15

Δ fopt
f21, 5-D
1e1
41
1e0
1157
1e-1
1674
1e-2
1692
1e-3
1705
1e-5
1729
1e-7
1757
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 2.2 (2)5.8 (6)8.0 (7)8.1 (5)8.0 (9)8.0 (8)8.0 (5)15/15
BIPOP-saACM-k loshchilov noiseless 2.7 (1)1.5 (1)4.1 (5)4.0 (9)4.0 (9)4.0 (0.7)3.9 (7)15/15
CGA-grid100 holtschulte noiseless 3.2 (5)170 (355)244 (717)318 (608)421 (226)647 (332)2119 (2063)0/15
CGA-grid16 holtschulte noiseless 2.6 (3)267 (808)414 (785)411 (591)420 (268)436 (326)963 (1311)2/15
CGA-ring100 holtschulte noiseless 5.3 (4)2.6 (1)3.5 (2)7.1 (3)11 (3)29 (14)81 (39)8/15
CGA-ring16 holtschulte noiseless 2.7 (0.9)95 (193)87 (251)86 (244)87 (42)95 (173)119 (149)9/15
CMAES Hutter hutter noiseless 2.2 (1)1.1 (1)2.1 (1)2.1 (4)2.1 (3)2.1 (2)4.3 (6)1/15
DE Pal pal noiseless 2.5 (2)1.9 (2)23 (60)24 (30)24 (60)24 (29)24 (17)11/15
GA-100 holtschulte noiseless 3.8 (4)65 (162)133 (187)133 (112)133 (147)139 (147)163 (197)8/15
HCMA loshchilov noiseless 1.2 (0.4)5.2 (21)11 (31)11 (4)11 (18)11 (33)11 (26)15/15
HILL holtschulte noiseless 6.8 (15)345 (378)416 (667)412 (412)411 (361)411 (803)428 (391)4/15
HMLSL pal noiseless 2.3 (2)0.88 (0.6)1.1 (2)1.1 (0.6)1.1 (1.0)1.1 (0.5)1.1 (0.2)15/15
IP-10DDr liao noiseless 1.6 (2)11 (10)14 (18)14 (10)14 (28)14 (28)14 (11)15/15
IP-500 liao noiseless 1.6 (1)8.6 (8)51 (169)51 (324)50 (6)50 (6)50 (11)15/15
IPOP400D auger noiseless 2.5 (2)5.2 (8)3.7 (5)3.6 (1)3.6 (4)3.6 (2)3.7 (3)5/15
IP liao noiseless 1.6 (1)8.7 (9)290 (9)362 (7)458 (735)452 (1448)445 (718)13/15
MEMPSODE voglis noiseless 5.0 (6)14 (34)11 (17)11 (16)10 (14)10 (10)14 (21)15/15
MLSL pal noiseless 2.8 (5)0.74 (0.8)1.3 (0.8)1.3 (1)1.3 (1)1.4 (2)1.4 (0.9)15/15
OQNLP pal noiseless 1.6 (0.6)1.3 (2)1.8 (3)1.8 (3)1.8 (5)1.8 (2)8.8 (9)2/15
P-DCN tran noiseless 1.9e4 (6)1.2e4 (2e4)5e60/15
P-zero tran noiseless 8713 (6e4)1.2e4 (2e4)5e60/15
PRCGA sawyerr noiseless 2.9 (2)31 (56)38 (66)39 (222)42 (14)52 (47)70 (49)13/15
SMAC-BBOB hutter noiseless 1.2 (0.8)0.48 (0.8)0.65 (0.4)1.4 (0.6)4.3 (3)5000/15
U-DCN tran noiseless 2.7 (3)435 (2405)906 (2987)897 (1626)892 (2200)885 (1556)880 (811)12/15
U-zero tran noiseless 2.9 (1)236 (200)1410 (2520)1395 (2433)1386 (1589)1375 (2433)1398 (2153)11/15
fmincon pal noiseless 2.6 (4)0.82 (1)0.94 (0.8)0.94 (2)0.95 (1.0)0.97 (1)1.0 (2)15/15
fminunc pal noiseless 2.3 (3)0.84 (1)0.98 (0.9)1.00 (1)1.0 (2)1.1 (0.4)1.1 (0.9)15/15
lmm-CMA-ES auger noiseless 2.1 (0.7)1.3 (1)1.5 (1)1.5 (1)1.6 (2)1.9 (2)1.9 (0.8)8/15
simplex pal noiseless 16 (15)2.3 (1)3.6 (4)3.5 (3)3.5 (2)3.5 (2)3.5 (3)15/15
tany liao noiseless 1.6 (1)3.8 (7)9.3 (8)9.3 (22)9.3 (22)9.2 (6)9.2 (24)15/15
texp liao noiseless 1.1 (0.6)13 (13)23 (13)23 (34)23 (52)23 (51)23 (48)15/15

Δ fopt
f22, 5-D
1e1
71
1e0
386
1e-1
938
1e-2
980
1e-3
1008
1e-5
1040
1e-7
1068
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 8.1 (12)20 (3)21 (26)21 (24)21 (31)20 (31)20 (25)15/15
BIPOP-saACM-k loshchilov noiseless 9.1 (15)6.5 (6)23 (10)23 (14)22 (56)21 (54)21 (51)15/15
CGA-grid100 holtschulte noiseless 5.5 (2)128 (200)544 (672)731 (833)1680 (1410)2e50/15
CGA-grid16 holtschulte noiseless 5.1 (12)686 (824)662 (440)1162 (574)3483 (2914)3458 (2885)2e50/15
CGA-ring100 holtschulte noiseless 5.5 (4)11 (13)36 (82)116 (94)201 (193)830 (822)2e50/15
CGA-ring16 holtschulte noiseless 2.5 (2)93 (308)320 (928)421 (257)753 (767)3374 (6130)3322 (3336)0/15
CMAES Hutter hutter noiseless 1.9 (1)4.3 (6)5060/15
DE Pal pal noiseless 3.5 (4)69 (4)96 (160)93 (52)92 (100)91 (192)90 (95)8/15
GA-100 holtschulte noiseless 5.9 (7)242 (325)439 (801)524 (198)525 (571)816 (598)2e50/15
HCMA loshchilov noiseless 3.3 (5)5.5 (11)13 (23)18 (30)17 (39)17 (12)24 (29)15/15
HILL holtschulte noiseless 6.7 (11)456 (908)321 (600)452 (488)731 (1110)2e50/15
HMLSL pal noiseless 3.6 (3)2.1 (2)1.3 (0.3)1.3 (0.7)1.3 (0.4)1.4 (1)1.5 (0.6)14/15
IP-10DDr liao noiseless 7.4 (11)42 (51)43 (59)41 (57)40 (37)39 (48)39 (37)15/15
IP-500 liao noiseless 7.4 (11)92 (293)580 (276)989 (1406)962 (2608)934 (2640)910 (4820)13/15
IPOP400D auger noiseless 4.9 (10)8.0 (8)14 (17)13 (12)13 (12)13 (17)12 (11)3/15
IP liao noiseless 7.4 (18)33 (78)1315 (3579)4602 (7653)5753 (6202)5580 (6017)5436 (8331)7/15
MEMPSODE voglis noiseless 4.6 (3)7.9 (6)42 (33)42 (18)41 (119)40 (115)52 (30)15/15
MLSL pal noiseless 2.7 (3)1.8 (1)1.4 (1)1.3 (2)1.3 (1)1.4 (1)1.5 (0.9)15/15
OQNLP pal noiseless 2.8 (3)2.5 (0.7)2.9 (7)2.8 (7)2.8 (4)2.7 (4)9.4 (14)2/15
P-DCN tran noiseless 2.6e4 (5e4)1.9e4 (6477)2.1e4 (2e4)2.0e4 (4e4)2.0e4 (4e4)1.9e4 (2e4)1.9e4 (3e4)3/15
P-zero tran noiseless 2.6e4 (4e4)3.6e4 (3e4)2.1e4 (3e4)2.0e4 (1e4)2.0e4 (2e4)1.9e4 (3e4)1.9e4 (3e4)3/15
PRCGA sawyerr noiseless 3.3 (3)110 (277)298 (498)416 (535)421 (280)888 (1044)2322 (3730)1/15
SMAC-BBOB hutter noiseless 0.90 (1.0)0.92 (0.6)3.7 (3)3.6 (4)7.4 (4)5000/15
U-DCN tran noiseless 1.9 (1)327 (1113)1145 (5377)1125 (2546)1129 (1667)1256 (2486)1469 (594)13/15
U-zero tran noiseless 4.8 (7)1107 (320)1458 (1510)1511 (2699)1832 (5163)5410 (3205)3.5e4 (5e4)0/15
fmincon pal noiseless 2.2 (3)1.3 (1)1.0 (1)0.99 (0.2)1.00 (0.8)1.1 (2)1.2 (0.3)15/15
fminunc pal noiseless 3.3 (3)1.2 (0.9)1.4 (2)1.4 (1)1.4 (2)1.5 (1)1.5 (1)15/15
lmm-CMA-ES auger noiseless 2.5 (6)3.8 (8)13 (19)13 (11)12 (13)12 (7)12 (12)3/15
simplex pal noiseless 11 (9)5.1 (4)3.3 (1)3.2 (3)3.1 (3)3.1 (3)3.0 (3)15/15
tany liao noiseless 12 (1.0)29 (63)91 (93)87 (115)85 (111)82 (63)80 (100)15/15
texp liao noiseless 22 (9)13 (24)18 (20)18 (11)18 (14)17 (15)17 (17)15/15

Δ fopt
f23, 5-D
1e1
3.0
1e0
518
1e-1
14249
1e-2
27890
1e-3
31654
1e-5
33030
1e-7
34256
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.8 (2)8.6 (6)1.7 (2)0.94 (0.6)0.93 (0.7)0.91 (0.8)0.90 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 2.0 (2)12 (11)1.0 (0.9)0.88 (1)0.79 (1.0)1.0 (1)1.1 (1)15/15
CGA-grid100 holtschulte noiseless 3.0 (2)60 (50)2e50/15
CGA-grid16 holtschulte noiseless 2.2 (4)40 (59)2e50/15
CGA-ring100 holtschulte noiseless 1.8 (2)23 (27)2e50/15
CGA-ring16 holtschulte noiseless 3.0 (2)26 (32)2e50/15
CMAES Hutter hutter noiseless 1.6 (2)5060/15
DE Pal pal noiseless 1.9 (3)31 (33)1e50/15
GA-100 holtschulte noiseless 2.3 (3)45 (23)2e50/15
HCMA loshchilov noiseless 8.1 (6)13 (11)1.2 (0.8)0.69 (0.4)0.63 (0.4)1.0 (1)1.1 (1)15/15
HILL holtschulte noiseless 2.5 (5)49 (88)2e50/15
HMLSL pal noiseless 9.2 (11)2.4 (2)1.7 (0.9)11 (7)45 (43)1e50/15
IP-10DDr liao noiseless 2.1 (2)7.2 (5)1.7 (4)1.1 (1)0.96 (2)0.94 (2)0.93 (0.5)15/15
IP-500 liao noiseless 2.1 (2)7.2 (5)2.0 (4)1.2 (3)1.1 (0.7)1.1 (2)1.1 (0.6)15/15
IPOP400D auger noiseless 4.8 (5)24 (20)2.8 (3)28130/15
IP liao noiseless 2.1 (2)7.2 (9)2.0 (4)1.2 (0.4)1.1 (0.6)1.1 (2)1.1 (0.5)15/15
MEMPSODE voglis noiseless 3.4 (2)3.4 (2)3.4 (3)3.8 (4)3.5 (1)11 (20)10 (28)15/15
MLSL pal noiseless 9.2 (10)1.9 (1)2.0 (2)9.2 (10)22 (23)1e50/15
OQNLP pal noiseless 29 (36)5.6 (8)8.0 (10)4e40/15
P-DCN tran noiseless 3.6 (4)3.2 (3)970 (1667)5e60/15
P-zero tran noiseless 3.6 (3)29 (33)2398 (2329)5e60/15
PRCGA sawyerr noiseless 1.9 (1)39 (19)201 (163)2e50/15
SMAC-BBOB hutter noiseless 1.6 (2)5000/15
U-DCN tran noiseless 3.4 (2)10 (19)5e60/15
U-zero tran noiseless 3.2 (2)43 (43)1527 (2067)5e60/15
fmincon pal noiseless 7.2 (4)1.6 (2)1.2 (1)3.8 (4)10 (5)1e50/15
fminunc pal noiseless 9.1 (22)10 (7)82 (100)8e40/15
lmm-CMA-ES auger noiseless 1.9 (2)10 (4)2.9 (2)1.5 (1.0)1.3 (2)1.3 (2)1.2 (1)1/15
simplex pal noiseless 63 (100)3.0 (2)2.2 (3)7.4 (3)23 (16)22 (35)43 (55)0/15
tany liao noiseless 1.7 (1)7.5 (4)5.2 (5)3.1 (2)2.7 (1)2.7 (2)2.6 (3)15/15
texp liao noiseless 3.0 (3)7.0 (4)6.4 (21)4.2 (4)3.8 (6)3.6 (3)3.5 (3)14/15

Δ fopt
f24, 5-D
1e1
1622
1e0
2.2e5
1e-1
6.4e6
1e-2
9.6e6
1e-3
9.6e6
1e-5
1.3e7
1e-7
1.3e7
#succ
3/15
BIPOP-aCMA-STEP loshchilov noiseless 2.5 (2)1.7 (1)0.62 (0.8)0.65 (1)0.90 (1.0)1.0 (0.6)1.0 (2)4/15
BIPOP-saACM-k loshchilov noiseless 2.1 (2)0.85 (1)0.86 (2)0.91 (2)0.90 (2)0.68 (0.7)0.68 (0.7)6/15
CGA-grid100 holtschulte noiseless 93 (58)2e50/15
CGA-grid16 holtschulte noiseless 106 (157)2e50/15
CGA-ring100 holtschulte noiseless 19 (14)2e50/15
CGA-ring16 holtschulte noiseless 13 (12)2e50/15
CMAES Hutter hutter noiseless 5060/15
DE Pal pal noiseless 9.5 (6)1e50/15
GA-100 holtschulte noiseless 15 (15)2e50/15
HCMA loshchilov noiseless 1.4 (0.7)2.7 (4)0.73 (0.8)0.88 (0.9)1.1 (1)0.80 (0.4)0.80 (1)5/15
HILL holtschulte noiseless 38 (76)2e50/15
HMLSL pal noiseless 1.8 (2)1e50/15
IP-10DDr liao noiseless 2.0 (1)104 (100)5e60/15
IP-500 liao noiseless 2.0 (2)5e60/15
IPOP400D auger noiseless 1.6 (2)0.19 (0.1)28050/15
IP liao noiseless 2.0 (2)5e60/15
MEMPSODE voglis noiseless 6.8 (8)4.4 (4)0.20 (0.1)0.27 (0.3)0.27 (0.3)0.20 (0.1)0.23 (0.1)9/15
MLSL pal noiseless 3.4 (2)4.2 (5)6e40/15
OQNLP pal noiseless 0.73 (0.3)0.17 (0.2)0.02 (0.0)0.01 (0.0)0.01 (0.0)0.01 (1e-2)0.01 (9e-3)2/15
P-DCN tran noiseless 1155 (1655)5e60/15
P-zero tran noiseless 5e60/15
PRCGA sawyerr noiseless 6.5 (37)3.0 (2)3e50/15
SMAC-BBOB hutter noiseless 5000/15
U-DCN tran noiseless 709 (972)5e60/15
U-zero tran noiseless 575 (1004)5e60/15
fmincon pal noiseless 3.0 (2)7e40/15
fminunc pal noiseless 5.8 (6)7e40/15
lmm-CMA-ES auger noiseless 0.88 (0.6)28060/15
simplex pal noiseless 13 (8)5.9 (6)9e40/15
tany liao noiseless 2.2 (1)20 (29)5e60/15
texp liao noiseless 1.4 (1)0.76 (1)0.50 (0.3)1.1 (2)1.1 (0.6)0.80 (1)0.80 (0.7)6/15

Previous dimension | Dimension = 10 | Next dimension

Δ fopt
f1, 10-D
1e1
22
1e0
23
1e-1
23
1e-2
23
1e-3
23
1e-5
23
1e-7
23
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.3 (0)4.8 (0.5)6.2 (0.2)7.8 (0)9.4 (0.5)12 (0)15 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 4.8 (0.4)5.8 (0.4)7.1 (0.7)8.7 (0.8)10 (1.0)13 (1)16 (1)15/15
CGA-grid100 holtschulte noiseless 93 (45)295 (69)781 (178)2322 (429)6459 (3839)5e50/15
CGA-grid16 holtschulte noiseless 23 (6)59 (18)155 (56)406 (137)1114 (475)9433 (2200)5e50/15
CGA-ring100 holtschulte noiseless 63 (28)217 (36)490 (94)1019 (144)1886 (135)5854 (2090)5e50/15
CGA-ring16 holtschulte noiseless 16 (5)43 (14)107 (16)223 (36)516 (199)3834 (1071)3.2e5 (5e5)0/15
CMAES Hutter hutter noiseless 5.0 (2)11 (2)18 (3)24 (2)30 (4)53 (24)10020/15
DE Pal pal noiseless 17 (4)52 (6)88 (12)126 (8)161 (10)232 (13)304 (16)15/15
GA-100 holtschulte noiseless 33 (9)97 (23)240 (49)536 (128)1235 (364)6645 (2239)5e50/15
HCMA loshchilov noiseless 1 (0)0.97 (0.0)0.97 (0.0)0.99 (0.1)0.99 (0.0)0.99 (0.0)0.99 (0.1)15/15
HILL holtschulte noiseless 5.5 (1)13 (6)42 (23)137 (72)442 (101)3990 (1506)3.2e5 (5e5)0/15
HMLSL pal noiseless 0.65 (0.2)1.4 (0.5)1.9 (0.1)2.0 (0.0)2.6 (0.2)3.5 (0.2)4.1 (0.6)15/15
IP-10DDr liao noiseless 5.0 (1)11 (1)17 (0.5)24 (2)29 (0.8)43 (2)56 (4)15/15
IP-500 liao noiseless 5.0 (1)11 (0.9)17 (2)24 (0.8)29 (2)43 (2)56 (3)15/15
IPOP400D auger noiseless 4.5 (3)10 (2)17 (2)23 (3)30 (3)42 (4)55 (4)15/15
IP liao noiseless 5.0 (1)11 (0.7)17 (2)24 (2)29 (2)43 (2)56 (3)15/15
MEMPSODE voglis noiseless 4.4 (0.5)4.5 (0.1)4.5 (0.1)4.5 (0.1)4.5 (0.2)4.5 (0.2)4.5 (0.2)15/15
MLSL pal noiseless 0.65 (0.1)1.4 (0.5)1.9 (0.2)2.0 (0.3)2.6 (0.2)3.5 (0.2)4.1 (0.7)15/15
OQNLP pal noiseless 1.4 (0)1.4 (0.0)1.8 (0.3)1.9 (0.2)2.0 (0.0)2.0 (0)2.0 (0.0)15/15
P-DCN tran noiseless 25 (10)46 (14)57 (11)72 (9)107 (20)378 (94)1282 (433)15/15
P-zero tran noiseless 26 (14)45 (20)53 (6)60 (21)73 (13)208 (57)1552 (640)15/15
PRCGA sawyerr noiseless 23 (8)60 (18)96 (18)139 (22)187 (27)544 (120)1145 (132)15/15
SMAC-BBOB hutter noiseless 0.93 (0.2)1.6 (0.3)2.8 (0.2)5.9 (2)10000/15
U-DCN tran noiseless 10 (5)64 (37)192 (36)395 (118)897 (276)2493 (2077)5557 (2609)15/15
U-zero tran noiseless 6.2 (3)29 (12)86 (29)247 (123)702 (257)7433 (1838)7.8e4 (4e4)15/15
fmincon pal noiseless 0.65 (0.2)1.4 (0.5)1.9 (0.1)2.0 (0.3)2.6 (0.2)3.5 (0.2)4.1 (0.6)15/15
fminunc pal noiseless 1.0 (0)1 (0)1 (0)1 (0)1 (0)1 (0)1 (0)15/15
lmm-CMA-ES auger noiseless 3.2 (0.1)3.9 (0.1)4.6 (0.2)5.2 (0.3)5.7 (0.3)7.1 (0.2)8.4 (0.5)15/15
simplex pal noiseless 73 (22)116 (22)150 (94)257 (241)317 (206)801 (503)1873 (2984)14/15
tany liao noiseless 5.5 (2)13 (0.9)19 (3)26 (2)33 (3)48 (4)63 (5)15/15
texp liao noiseless 3.8 (1)11 (2)18 (3)25 (3)31 (2)45 (2)60 (3)15/15

Δ fopt
f2, 10-D
1e1
187
1e0
190
1e-1
191
1e-2
191
1e-3
193
1e-5
194
1e-7
195
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (0.1)1.5 (0.1)1.7 (0.2)1.9 (0.2)2.1 (0.1)2.4 (0.2)2.7 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 2.9 (0.3)3.1 (0.3)3.3 (0.1)3.5 (0.2)3.7 (0.2)4.1 (0.2)4.5 (0.3)15/15
CGA-grid100 holtschulte noiseless 815 (620)2413 (1468)1.9e4 (2e4)5e50/15
CGA-grid16 holtschulte noiseless 188 (109)587 (525)2668 (1761)1.9e4 (2e4)5e50/15
CGA-ring100 holtschulte noiseless 207 (60)367 (158)1181 (398)7040 (4724)5e50/15
CGA-ring16 holtschulte noiseless 164 (83)394 (384)1403 (1808)4487 (7131)5e50/15
CMAES Hutter hutter noiseless 10020/15
DE Pal pal noiseless 17 (0.6)21 (0.9)25 (1)30 (1)34 (1)42 (1)51 (2)15/15
GA-100 holtschulte noiseless 128 (50)493 (419)1662 (1082)5e50/15
HCMA loshchilov noiseless 1.3 (0.1)1.5 (0.2)1.7 (0.0)1.9 (0.1)2.1 (0.2)2.4 (0.2)2.7 (0.2)15/15
HILL holtschulte noiseless 120 (116)517 (335)2212 (2170)1.2e4 (1e4)3.8e4 (5e4)5e50/15
HMLSL pal noiseless 3.0 (0.9)3.3 (0.8)3.5 (2)3.7 (1)4.0 (1)5.4 (2)10 (7)15/15
IP-10DDr liao noiseless 22 (5)25 (4)28 (3)30 (3)30 (2)32 (0.7)33 (1)15/15
IP-500 liao noiseless 22 (2)25 (5)28 (3)30 (1)30 (3)32 (1)33 (2)15/15
IPOP400D auger noiseless 22 (4)26 (21)52 (38)75 (57)186 (180)48030/15
IP liao noiseless 22 (4)25 (4)28 (2)30 (2)30 (2)32 (1)33 (2)15/15
MEMPSODE voglis noiseless 1.6 (0.3)1.7 (0.2)1.7 (0.2)1.9 (0.5)2.0 (0.5)2.1 (0.3)★22.3 (0.3)★215/15
MLSL pal noiseless 3.0 (0.9)3.3 (0.8)3.5 (1)3.7 (2)4.0 (0.7)5.4 (1)7.9 (4)15/15
OQNLP pal noiseless 3.0 (1)3.6 (1.0)3.9 (0.9)4.0 (0.7)4.1 (1)4.3 (0.8)520 (632)0/15
P-DCN tran noiseless 19 (7)24 (10)41 (12)109 (93)148 (74)394 (364)2287 (1357)14/15
P-zero tran noiseless 16 (5)23 (8)49 (18)127 (73)287 (261)5781 (4341)7.2e4 (1e5)2/15
PRCGA sawyerr noiseless 18 (3)29 (5)95 (55)478 (1114)724 (280)2059 (1924)4246 (4465)10/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 94 (27)182 (160)320 (250)421 (245)1306 (5598)1.2e4 (3700)4.7e4 (2e5)7/15
U-zero tran noiseless 183 (212)577 (386)2651 (3368)7119 (4080)2.1e4 (1e4)2.4e5 (4e5)1e70/15
fmincon pal noiseless 3.1 (1)3.3 (2)3.5 (1)3.8 (1)4.2 (2)5.6 (3)12 (3)15/15
fminunc pal noiseless 10 (2)12 (3)13 (2)14 (1)14 (2)14 (2)15 (2)15/15
lmm-CMA-ES auger noiseless 4.8 (1)5.5 (1)6.0 (0.9)6.3 (1)6.5 (0.6)7.0 (0.7)7.5 (0.8)15/15
simplex pal noiseless 2928 (3256)2e50/15
tany liao noiseless 22 (4)26 (3)27 (2)29 (5)30 (2)31 (2)33 (2)15/15
texp liao noiseless 19 (4)23 (5)25 (3)27 (1)28 (1)30 (1)31 (2)15/15

Δ fopt
f3, 10-D
1e1
1739
1e0
3600
1e-1
3609
1e-2
3636
1e-3
3642
1e-5
3646
1e-7
3651
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.28 (0.0)0.29 (0.0)0.33 (0.0)0.34 (0.0)0.36 (0.1)0.38 (0.0)0.41 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 2.9 (2)429 (490)3693 (2057)3666 (3460)3660 (7880)3656 (2643)3652 (5541)8/15
CGA-grid100 holtschulte noiseless 15 (2)32 (8)87 (28)5e50/15
CGA-grid16 holtschulte noiseless 2.4 (0.5)6.5 (2)17 (5)52 (17)494 (644)5e50/15
CGA-ring100 holtschulte noiseless 7.1 (1)8.8 (2)16 (2)31 (8)78 (27)5e50/15
CGA-ring16 holtschulte noiseless 1.3 (0.4)2.2 (1)6.1 (2)22 (5)78 (51)5e50/15
CMAES Hutter hutter noiseless 8.6 (8)10020/15
DE Pal pal noiseless 10 (3)8.2 (0.8)29 (56)29 (42)29 (42)29 (28)30 (14)11/15
GA-100 holtschulte noiseless 3.2 (0.7)5.2 (2)13 (3)30 (6)112 (25)5e50/15
HCMA loshchilov noiseless 0.28 (0.0)0.29 (0.0)0.33 (0.1)0.34 (0.0)0.36 (0.0)0.38 (0.0)0.41 (0.0)15/15
HILL holtschulte noiseless 0.70 (0.3)1.8 (0.9)5.6 (2)18 (5)69 (17)5e50/15
HMLSL pal noiseless 4.5 (3)10 (3)39 (83)39 (15)39 (83)39 (57)39 (96)10/15
IP-10DDr liao noiseless 3.7 (3)161 (272)1049 (1474)1042 (1692)1040 (1147)1040 (1304)1039 (1442)13/15
IP-500 liao noiseless 3.7 (4)92 (85)567 (974)563 (700)563 (699)563 (863)563 (485)15/15
IPOP400D auger noiseless 12 (11)48150/15
IP liao noiseless 3.7 (3)4187 (5558)3.9e4 (4e4)3.9e4 (3e4)3.8e4 (2e4)3.8e4 (9e4)3.8e4 (4e4)1/15
MEMPSODE voglis noiseless 6.8 (3)16 (12)28 (15)28 (11)28 (11)29 (14)32 (17)15/15
MLSL pal noiseless 2e50/15
OQNLP pal noiseless 273 (157)7e40/15
P-DCN tran noiseless 83 (110)273 (347)389 (252)386 (491)385 (399)386 (438)396 (446)15/15
P-zero tran noiseless 178 (223)433 (370)977 (685)970 (647)969 (678)973 (525)1021 (600)15/15
PRCGA sawyerr noiseless 2.6 (0.7)9.4 (9)13 (10)16 (12)18 (12)55 (66)94 (95)12/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 1.6 (1)6.1 (2)8.9 (2)16 (4)20 (11)68 (109)672 (1131)14/15
U-zero tran noiseless 1.1 (0.5)3.3 (0.7)11 (4)40 (19)144 (93)1100 (749)1e70/15
fmincon pal noiseless 2e50/15
fminunc pal noiseless 2e50/15
lmm-CMA-ES auger noiseless 2.0 (2)48080/15
simplex pal noiseless 2e50/15
tany liao noiseless 2.5 (3)151 (210)1042 (1132)1034 (1163)1033 (989)1033 (1590)1032 (618)14/15
texp liao noiseless 3.2 (2)230 (251)1441 (1015)1431 (1573)1429 (2003)1428 (1259)1426 (1275)14/15

Δ fopt
f4, 10-D
1e1
2234
1e0
3626
1e-1
3660
1e-2
3695
1e-3
3707
1e-5
3744
1e-7
28767
#succ
12/15
BIPOP-aCMA-STEP loshchilov noiseless 0.24 (0.0)0.63 (0.1)0.88 (0.2)1.1 (0.2)1.4 (0.2)1.7 (0.2)0.25 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 4.2 (4)1e70/15
CGA-grid100 holtschulte noiseless 15 (7)42 (6)264 (282)5e50/15
CGA-grid16 holtschulte noiseless 2.5 (0.8)8.5 (3)25 (9)83 (30)994 (1409)5e50/15
CGA-ring100 holtschulte noiseless 6.5 (1)11 (1)18 (4)37 (8)81 (21)5e50/15
CGA-ring16 holtschulte noiseless 1.4 (0.1)3.3 (1.0)8.9 (3)31 (21)91 (48)5e50/15
CMAES Hutter hutter noiseless 10020/15
DE Pal pal noiseless 8.0 (1)46 (43)774 (505)767 (704)765 (1066)758 (334)99 (101)1/15
GA-100 holtschulte noiseless 3.2 (0.5)7.0 (2)16 (6)40 (15)253 (225)5e50/15
HCMA loshchilov noiseless 0.24 (0.0)0.63 (0.2)0.88 (0.1)1.1 (0.1)1.4 (0.2)1.7 (0.2)0.25 (0.0)15/15
HILL holtschulte noiseless 0.64 (0.2)2.7 (2)8.6 (2)40 (18)132 (77)5e50/15
HMLSL pal noiseless 4.6 (2)234 (179)2e50/15
IP-10DDr liao noiseless 5.6 (5)1e70/15
IP-500 liao noiseless 5.6 (4)1e70/15
IPOP400D auger noiseless 32 (29)48050/15
IP liao noiseless 5.6 (3)1e70/15
MEMPSODE voglis noiseless 8.1 (2)28 (23)81 (64)80 (28)80 (95)80 (31)13 (17)15/15
MLSL pal noiseless 2e50/15
OQNLP pal noiseless 7e40/15
P-DCN tran noiseless 101 (47)147 (106)218 (225)216 (200)216 (155)215 (190)29 (27)15/15
P-zero tran noiseless 123 (51)275 (480)632 (499)626 (446)624 (477)625 (463)95 (51)15/15
PRCGA sawyerr noiseless 3.7 (0.7)12 (6)20 (12)21 (9)24 (12)57 (14)12 (2)12/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 1.8 (0.4)9.4 (1)12 (3)16 (8)39 (10)76 (39)74 (94)9/15
U-zero tran noiseless 1.1 (0.6)5.0 (3)17 (13)63 (41)191 (58)1620 (640)1e70/15
fmincon pal noiseless 2e50/15
fminunc pal noiseless 2e50/15
lmm-CMA-ES auger noiseless 10 (11)48130/15
simplex pal noiseless 2e50/15
tany liao noiseless 6.3 (4)1e70/15
texp liao noiseless 5.5 (2)1e70/15

Δ fopt
f5, 10-D
1e1
20
1e0
20
1e-1
20
1e-2
20
1e-3
20
1e-5
20
1e-7
20
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)1.1 (0)15/15
BIPOP-saACM-k loshchilov noiseless 4.7 (0.8)6.0 (1)6.1 (1)6.1 (0.7)6.1 (0.7)6.1 (1)6.1 (1)15/15
CGA-grid100 holtschulte noiseless 222 (86)348 (158)385 (91)389 (132)389 (94)389 (144)389 (119)15/15
CGA-grid16 holtschulte noiseless 41 (9)64 (11)70 (9)70 (7)70 (9)70 (9)70 (13)15/15
CGA-ring100 holtschulte noiseless 152 (28)214 (31)245 (30)248 (36)248 (26)248 (21)248 (24)15/15
CGA-ring16 holtschulte noiseless 28 (6)41 (11)45 (11)46 (10)46 (11)46 (10)46 (8)15/15
CMAES Hutter hutter noiseless 4.4 (0.4)5.6 (0.6)5.9 (0.9)5.9 (1)5.9 (1.0)5.9 (1)5.9 (1)15/15
DE Pal pal noiseless 119 (15)327 (32)556 (43)785 (20)1024 (38)1488 (54)1965 (60)15/15
GA-100 holtschulte noiseless 81 (12)119 (14)130 (23)133 (19)133 (22)133 (19)133 (15)15/15
HCMA loshchilov noiseless 1.2 (0.1)1.5 (0.5)1.6 (0.4)1.6 (0.5)1.6 (0.4)1.6 (0.5)1.6 (0.3)15/15
HILL holtschulte noiseless 8.0 (5)11 (2)12 (6)12 (2)12 (4)12 (4)12 (5)15/15
HMLSL pal noiseless 2.8 (0)5.0 (0)6.1 (0)6.1 (0)6.7 (0)7.2 (0)1812 (1181)15/15
IP-10DDr liao noiseless 13 (7)63 (33)87 (45)105 (51)124 (54)161 (78)185 (71)15/15
IP-500 liao noiseless 13 (4)63 (22)87 (37)105 (46)124 (43)161 (45)185 (79)15/15
IPOP400D auger noiseless 5.0 (0.9)6.2 (0.6)6.3 (1)6.3 (1)6.3 (1)6.3 (1)6.3 (1)15/15
IP liao noiseless 13 (2)63 (32)87 (31)105 (39)124 (49)161 (72)185 (62)15/15
MEMPSODE voglis noiseless 6.4 (2)6.5 (2)6.5 (1)6.5 (2)6.5 (2)6.5 (2)6.5 (2)15/15
MLSL pal noiseless 2.8 (0)5.0 (0)6.1 (0)6.1 (0)6.7 (0)7.2 (0)89 (64)11/15
OQNLP pal noiseless 1.6 (0)1.7 (0)1.7 (0)1.7 (0)1.7 (0)1.7 (0)1.7 (0)15/15
P-DCN tran noiseless 83 (20)145 (54)161 (65)178 (64)205 (32)278 (55)357 (77)15/15
P-zero tran noiseless 76 (28)121 (50)132 (47)139 (40)144 (75)162 (49)180 (90)15/15
PRCGA sawyerr noiseless 1617 (721)3231 (1906)5425 (5255)3.7e4 (6e4)2.2e5 (2e5)5e50/15
SMAC-BBOB hutter noiseless 0.60 (0.1)★40.63 (0.1)★40.63 (0.1)★40.63 (0.1)★40.63 (0.1)★40.63 (0.2)★40.63 (0.1)★415/15
U-DCN tran noiseless 69 (19)520 (179)1557 (354)5083 (6575)2.0e4 (4933)5.1e5 (4e5)1e70/15
U-zero tran noiseless 42 (12)476 (270)6667 (3269)6.8e4 (2e4)7.3e6 (7e6)1e70/15
fmincon pal noiseless 2.8 (0)5.0 (0)6.1 (0)6.1 (0)6.7 (0)7.2 (0)77 (44)11/15
fminunc pal noiseless 1.7 (0)2.8 (0)2.8 (0)2.8 (0)2.8 (0)2.8 (0)2.8 (0)15/15
lmm-CMA-ES auger noiseless 5.2 (2)6.2 (0.8)6.5 (2)6.5 (1)6.5 (3)6.5 (3)6.5 (1)15/15
simplex pal noiseless 108 (54)143 (93)144 (124)144 (86)144 (136)144 (91)144 (118)15/15
tany liao noiseless 16 (18)46 (29)71 (35)86 (39)102 (36)133 (67)158 (60)15/15
texp liao noiseless 29 (14)73 (73)99 (72)123 (57)148 (79)193 (123)226 (147)15/15

Δ fopt
f6, 10-D
1e1
412
1e0
623
1e-1
826
1e-2
1039
1e-3
1292
1e-5
1841
1e-7
2370
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.9 (0.5)1.9 (0.3)1.8 (0.2)1.8 (0.2)1.7 (0.2)1.7 (0.2)1.6 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 2.0 (0.4)2.1 (0.3)2.1 (0.6)2.2 (0.3)2.0 (0.7)2.0 (0.5)2.0 (0.4)15/15
CGA-grid100 holtschulte noiseless 107 (128)694 (284)5e50/15
CGA-grid16 holtschulte noiseless 32 (107)208 (276)1341 (2123)1645 (2067)5e50/15
CGA-ring100 holtschulte noiseless 35 (11)92 (41)233 (162)1044 (1136)5768 (3676)5e50/15
CGA-ring16 holtschulte noiseless 7.5 (2)25 (20)380 (339)1143 (733)5722 (4644)5e50/15
CMAES Hutter hutter noiseless 1.7 (0.5)5.8 (5)10020/15
DE Pal pal noiseless 10 (4)16 (7)22 (5)25 (5)27 (9)28 (7)30 (8)15/15
GA-100 holtschulte noiseless 17 (4)45 (22)217 (222)957 (914)5688 (5418)5e50/15
HCMA loshchilov noiseless 2.3 (0.8)2.4 (0.6)2.6 (0.8)2.7 (1)2.5 (0.7)2.4 (0.8)2.4 (0.9)15/15
HILL holtschulte noiseless 11 (21)152 (152)1364 (1813)3320 (3128)5683 (7740)5e50/15
HMLSL pal noiseless 1.4 (0.3)1.3 (0.4)1.4 (0.3)1.6 (0.6)1.7 (0.8)1.9 (0.8)2.1 (0.7)15/15
IP-10DDr liao noiseless 1.4 (0.3)1.6 (0.2)1.7 (0.3)1.8 (0.3)1.7 (0.1)1.7 (0.1)1.6 (0.1)15/15
IP-500 liao noiseless 1.4 (0.2)1.6 (0.2)1.7 (0.1)1.8 (0.1)1.7 (0.2)1.7 (0.1)1.6 (0.1)15/15
IPOP400D auger noiseless 1.7 (0.4)1.8 (0.3)1.8 (0.2)1.8 (0.3)1.7 (0.2)1.6 (0.1)1.6 (0.1)15/15
IP liao noiseless 1.4 (0.2)1.6 (0.2)1.7 (0.2)1.8 (0.3)1.7 (0.2)1.7 (0.1)1.6 (0.1)15/15
MEMPSODE voglis noiseless 1.9 (1)2.8 (4)3.6 (4)7.7 (5)7.9 (4)8.7 (1)25 (16)15/15
MLSL pal noiseless 1.4 (0.7)1.3 (0.2)1.4 (0.7)1.6 (0.5)1.7 (0.5)1.9 (0.6)2.1 (0.6)15/15
OQNLP pal noiseless 1.00 (0.6)1.2 (0.3)1.7 (0.8)3.6 (8)13 (14)1051 (1185)1e50/15
P-DCN tran noiseless 8.7 (2)9.0 (4)10 (5)408 (30)1080 (3558)1252 (1616)1986 (3921)10/15
P-zero tran noiseless 69 (10)82 (25)438 (1274)1572 (2552)2178 (2099)5931 (4083)2.9e4 (5e4)1/15
PRCGA sawyerr noiseless 15 (14)330 (507)886 (687)2927 (1970)1.1e4 (1e4)1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 35 (52)205 (276)1114 (1221)1681 (3181)2528 (3326)6430 (4231)1.9e4 (4e4)0/15
U-zero tran noiseless 1463 (190)4443 (2e4)8343 (7590)2.9e4 (4e4)3.3e4 (3e4)1e70/15
fmincon pal noiseless 1.3 (0.4)1.3 (0.4)1.4 (0.6)1.5 (0.4)1.6 (0.4)1.9 (0.2)2.2 (0.4)15/15
fminunc pal noiseless 2.4 (1)3.2 (0.7)3.9 (0.8)3.9 (1)3.9 (0.8)4.1 (0.6)65 (68)1/15
lmm-CMA-ES auger noiseless 5.5 (4)17 (21)48040/15
simplex pal noiseless 273 (94)2e50/15
tany liao noiseless 1.5 (0.3)1.7 (0.5)1.8 (0.2)1.9 (0.3)1.8 (0.2)1.8 (0.2)1.7 (0.1)15/15
texp liao noiseless 1.6 (0.3)1.9 (0.2)2.1 (0.1)2.1 (0.2)2.1 (0.2)2.0 (0.1)1.9 (0.2)15/15

Δ fopt
f7, 10-D
1e1
172
1e0
1611
1e-1
4195
1e-2
5099
1e-3
5141
1e-5
5141
1e-7
5389
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.2 (0.5)1.4 (1)0.93 (0.4)0.86 (0.2)0.87 (0.3)0.87 (0.3)0.85 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 1.4 (0.5)0.71 (1.0)0.46 (0.2)0.52 (0.3)0.53 (0.4)0.53 (0.3)0.53 (0.3)15/15
CGA-grid100 holtschulte noiseless 349 (165)2281 (1241)5e50/15
CGA-grid16 holtschulte noiseless 87 (258)2228 (2948)5e50/15
CGA-ring100 holtschulte noiseless 36 (10)135 (270)1755 (1520)5e50/15
CGA-ring16 holtschulte noiseless 14 (5)661 (1105)5e50/15
CMAES Hutter hutter noiseless 2.1 (0.6)2.9 (2)3.6 (4)10020/15
DE Pal pal noiseless 12 (5)6.1 (2)5.6 (2)7.0 (6)7.3 (5)7.3 (6)7.3 (2)15/15
GA-100 holtschulte noiseless 14 (2)205 (169)802 (995)5e50/15
HCMA loshchilov noiseless 2.2 (0.6)0.79 (0.7)0.55 (0.5)0.64 (0.4)0.68 (0.7)0.68 (0.7)0.70 (0.4)15/15
HILL holtschulte noiseless 70 (208)1341 (1785)5e50/15
HMLSL pal noiseless 17 (6)8.2 (4)7.5 (4)9.5 (3)10 (3)10 (6)10 (10)15/15
IP-10DDr liao noiseless 2.2 (0.5)2.1 (2)1.6 (0.5)1.6 (0.6)1.6 (0.4)1.6 (0.7)1.6 (0.7)15/15
IP-500 liao noiseless 2.2 (0.7)2.1 (2)1.6 (0.7)1.6 (0.5)1.6 (0.7)1.6 (0.7)1.6 (0.8)15/15
IPOP400D auger noiseless 1.9 (0.6)1.1 (1)8.4 (11)14 (18)14 (17)14 (15)13 (15)1/15
IP liao noiseless 2.2 (0.6)2.1 (1)1.6 (1)1.6 (0.3)1.6 (0.5)1.6 (1)1.6 (0.4)15/15
MEMPSODE voglis noiseless 48 (20)28 (35)32 (37)35 (53)35 (25)35 (41)41 (37)15/15
MLSL pal noiseless 1e50/15
OQNLP pal noiseless 160 (209)55090/15
P-DCN tran noiseless 336 (596)5066 (6890)3.3e4 (3e4)2.7e4 (5e4)2.7e4 (5e4)2.7e4 (1e4)2.6e4 (3e4)1/15
P-zero tran noiseless 914 (773)2345 (3758)3094 (4029)2641 (2252)2619 (3479)2619 (4138)2499 (2402)8/15
PRCGA sawyerr noiseless 12 (7)609 (551)871 (890)5e50/15
SMAC-BBOB hutter noiseless 1.2 (0.1)0.74 (0.4)3.6 (6)10000/15
U-DCN tran noiseless 2091 (7633)9593 (2e4)3.3e4 (3e4)1e70/15
U-zero tran noiseless 283 (116)6498 (9650)1.7e4 (2e4)1e70/15
fmincon pal noiseless 1e50/15
fminunc pal noiseless 1e50/15
lmm-CMA-ES auger noiseless 1.1 (0.2)1.7 (1)2.8 (1)4.4 (2)4.4 (5)4.4 (2)4.2 (6)2/15
simplex pal noiseless 2919 (2059)1e50/15
tany liao noiseless 2.1 (0.7)1.9 (1)1.4 (0.7)1.2 (0.8)1.3 (0.8)1.3 (0.5)1.3 (0.3)15/15
texp liao noiseless 2.0 (0.8)2.4 (2)1.4 (0.6)1.4 (0.6)1.4 (0.6)1.4 (0.6)1.3 (0.6)15/15

Δ fopt
f8, 10-D
1e1
326
1e0
921
1e-1
1114
1e-2
1217
1e-3
1267
1e-5
1315
1e-7
1343
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.1 (0.3)3.6 (0.6)3.8 (0.6)3.7 (0.4)3.8 (0.4)3.9 (0.6)4.0 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 1.3 (0.4)1.4 (0.2)1.3 (0.2)1.3 (0.3)1.3 (0.1)1.3 (0.2)1.4 (0.2)15/15
CGA-grid100 holtschulte noiseless 259 (256)2541 (3438)5e50/15
CGA-grid16 holtschulte noiseless 79 (24)900 (712)1954 (1908)6049 (8833)5e50/15
CGA-ring100 holtschulte noiseless 64 (14)734 (558)1396 (1049)5938 (5341)5e50/15
CGA-ring16 holtschulte noiseless 20 (21)3569 (4479)5e50/15
CMAES Hutter hutter noiseless 2.1 (1)10020/15
DE Pal pal noiseless 10 (2)31 (55)31 (46)32 (42)33 (2)36 (2)40 (1)14/15
GA-100 holtschulte noiseless 43 (16)5e50/15
HCMA loshchilov noiseless 1.7 (0.3)1.7 (1.0)1.6 (0.2)1.6 (0.2)1.6 (0.7)1.6 (0.8)1.6 (0.1)15/15
HILL holtschulte noiseless 16 (10)384 (277)1848 (2013)5e50/15
HMLSL pal noiseless 0.83 (0.4)1.4 (2)1.3 (3)1.2 (0.2)1.2 (3)1.2 (2)1.2 (0.1)15/15
IP-10DDr liao noiseless 2.4 (0.4)5.1 (3)5.1 (0.5)5.0 (2)5.1 (0.6)5.2 (1)5.3 (0.6)15/15
IP-500 liao noiseless 2.4 (0.9)5.1 (1.0)5.1 (1.0)5.0 (0.4)5.1 (0.7)5.2 (0.5)5.3 (0.6)15/15
IPOP400D auger noiseless 2.1 (2)6.0 (4)6.4 (5)9.2 (7)11 (21)27 (19)26 (24)2/15
IP liao noiseless 2.4 (0.4)5.1 (1)5.1 (0.2)5.0 (0.6)5.1 (2)5.2 (2)5.3 (2)15/15
MEMPSODE voglis noiseless 0.96 (0.4)2.0 (3)1.9 (1)1.9 (2)1.9 (2)1.9 (1)1.9 (1)15/15
MLSL pal noiseless 0.83 (0.3)0.91 (0.7)0.84 (0.7)0.81 (0.7)0.80 (0.6)0.80 (0.2)0.80 (0.6)15/15
OQNLP pal noiseless 0.73 (0.1)0.80 (0.4)0.76 (0.5)0.74 (0.3)0.73 (0.5)0.73 (0.4)431 (701)0/15
P-DCN tran noiseless 37 (111)5847 (5602)5381 (2e4)5728 (4180)6677 (7901)9246 (8203)1e70/15
P-zero tran noiseless 5.7 (2)1866 (2819)2130 (9039)5269 (276)1e70/15
PRCGA sawyerr noiseless 33 (29)2290 (2986)5986 (7415)1.2e4 (2e4)1e60/15
SMAC-BBOB hutter noiseless 10 (11)10000/15
U-DCN tran noiseless 51 (23)734 (680)1719 (1216)3366 (1358)5316 (1263)1e70/15
U-zero tran noiseless 35 (31)6901 (9883)5.8e4 (7e4)1.2e5 (2e5)1e70/15
fmincon pal noiseless 0.83 (0.4)0.91 (0.1)0.84 (0.4)0.81 (0.6)0.80 (0.3)0.81 (0.6)0.81 (0.1)15/15
fminunc pal noiseless 1.3 (0.8)1.2 (0.2)1.1 (0.2)1.0 (0.2)1.0 (0.2)1.00 (0.2)0.99 (0.2)15/15
lmm-CMA-ES auger noiseless 1.2 (0.1)1.5 (0.2)1.5 (0.3)1.4 (0.3)1.4 (0.2)1.5 (0.2)1.5 (0.2)15/15
simplex pal noiseless 26 (20)222 (422)2e50/15
tany liao noiseless 2.2 (0.4)4.7 (0.9)4.8 (0.9)4.8 (0.9)4.8 (0.9)5.0 (0.9)5.1 (0.9)15/15
texp liao noiseless 2.0 (0.7)4.6 (0.9)4.7 (0.6)4.7 (0.6)4.8 (0.4)4.9 (0.5)5.1 (0.5)15/15

Δ fopt
f9, 10-D
1e1
200
1e0
648
1e-1
857
1e-2
993
1e-3
1065
1e-5
1138
1e-7
1185
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.5 (1)5.8 (3)5.3 (1)5.0 (4)4.9 (2)4.9 (0.7)5.0 (2)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (0.9)2.1 (0.3)1.9 (0.7)1.7 (0.2)1.7 (0.2)1.6 (0.2)1.6 (0.2)15/15
CGA-grid100 holtschulte noiseless 540 (124)5e50/15
CGA-grid16 holtschulte noiseless 788 (1879)5e50/15
CGA-ring100 holtschulte noiseless 133 (32)5208 (5015)5e50/15
CGA-ring16 holtschulte noiseless 210 (15)5e50/15
CMAES Hutter hutter noiseless 2.8 (0.4)10020/15
DE Pal pal noiseless 21 (9)206 (191)457 (370)3003 (3676)2e50/15
GA-100 holtschulte noiseless 72 (17)5e50/15
HCMA loshchilov noiseless 2.4 (0.9)2.2 (0.3)1.9 (0.3)1.8 (0.2)1.7 (0.2)1.7 (0.6)1.7 (0.2)15/15
HILL holtschulte noiseless 216 (673)1.1e4 (1e4)5e50/15
HMLSL pal noiseless 0.49 (0.1)0.48 (0.0)0.48 (0.0)0.47 (0.0)0.46 (0.0)0.46 (0.0)0.46 (0.0)15/15
IP-10DDr liao noiseless 3.4 (1)6.6 (1)6.2 (1)5.9 (0.3)5.7 (0.9)5.7 (0.8)5.8 (1)15/15
IP-500 liao noiseless 3.4 (0.8)6.6 (1.0)6.2 (0.8)5.9 (0.7)5.7 (0.7)5.7 (0.5)5.8 (0.7)15/15
IPOP400D auger noiseless 3.1 (4)7.3 (6)8.0 (6)18 (28)23 (14)48030/15
IP liao noiseless 3.4 (0.7)6.6 (1)6.2 (0.7)5.9 (0.8)5.7 (0.6)5.7 (1)5.8 (0.9)15/15
MEMPSODE voglis noiseless 1.8 (0.4)4.1 (7)3.7 (4)3.4 (0.5)3.2 (6)3.3 (4)3.3 (3)15/15
MLSL pal noiseless 0.49 (0.1)0.48 (0.0)0.48 (0.0)0.47 (0.0)0.46 (0.0)0.46 (0.0)0.46 (0.0)15/15
OQNLP pal noiseless 0.86 (5e-3)0.39 (9e-3)0.42 (9e-3)0.42 (7e-3)0.42 (7e-3)0.42 (7e-3)4.5 (2)7/15
P-DCN tran noiseless 414 (1492)3568 (901)5581 (1092)1.9e4 (1e4)1.4e5 (1e5)1e70/15
P-zero tran noiseless 1103 (5)8638 (2e4)9056 (9053)1e70/15
PRCGA sawyerr noiseless 20 (9)5077 (5266)1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 4841 (1e4)9103 (1e4)1.4e4 (1e4)1e70/15
U-zero tran noiseless 4133 (1854)3.7e4 (2e4)1e70/15
fmincon pal noiseless 0.49 (0.0)0.48 (0.1)0.48 (0.0)0.46 (0.0)0.46 (0.0)0.45 (0.0)0.46 (0.0)15/15
fminunc pal noiseless 0.40 (0.0)0.39 (0.0)0.41 (6e-3)0.41 (0.0)0.41 (8e-3)0.41 (0.0)0.40 (0.0)15/15
lmm-CMA-ES auger noiseless 1.6 (0.2)2.1 (3)1.9 (1)1.9 (3)1.8 (1)1.8 (2)1.8 (2)14/15
simplex pal noiseless 79 (103)625 (742)3456 (4394)2983 (2123)2e50/15
tany liao noiseless 3.1 (0.5)6.3 (0.6)6.1 (0.6)5.8 (0.5)5.7 (0.4)5.7 (0.5)5.7 (0.4)15/15
texp liao noiseless 2.5 (0.5)6.5 (0.9)6.3 (2)5.9 (1)5.8 (0.8)5.8 (0.6)5.9 (0.4)15/15

Δ fopt
f10, 10-D
1e1
1835
1e0
2172
1e-1
2455
1e-2
2728
1e-3
2802
1e-5
4543
1e-7
4739
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.5 (0.2)1.5 (0.3)1.4 (0.1)1.4 (0.1)1.4 (0.1)0.91 (0.1)0.94 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 0.29 (0.0)0.27 (0.0)0.25 (0.0)0.24 (0.0)0.25 (0.0)0.17 (0.0)0.18 (0.0)★315/15
CGA-grid100 holtschulte noiseless 5e50/15
CGA-grid16 holtschulte noiseless 5e50/15
CGA-ring100 holtschulte noiseless 5e50/15
CGA-ring16 holtschulte noiseless 5e50/15
CMAES Hutter hutter noiseless 10020/15
DE Pal pal noiseless 2e50/15
GA-100 holtschulte noiseless 5e50/15
HCMA loshchilov noiseless 0.38 (0.0)0.34 (0.0)0.32 (0.0)0.31 (0.0)0.31 (0.0)0.21 (0.0)0.22 (0.0)15/15
HILL holtschulte noiseless 5e50/15
HMLSL pal noiseless 0.23 (0.2)0.22 (0.1)0.21 (0.1)0.20 (0.1)0.21 (0.1)9.2 (33)600 (1036)0/15
IP-10DDr liao noiseless 2.2 (0.4)2.2 (0.4)2.2 (0.2)2.1 (0.1)2.1 (0.2)1.3 (0.1)1.4 (0.1)15/15
IP-500 liao noiseless 2.2 (0.3)2.2 (0.5)2.2 (0.3)2.1 (0.2)2.1 (0.2)1.3 (0.1)1.4 (0.1)15/15
IPOP400D auger noiseless 2.3 (0.3)4.6 (3)15 (26)48030/15
IP liao noiseless 2.2 (0.4)2.2 (0.3)2.2 (0.3)2.1 (0.2)2.1 (0.1)1.3 (0.1)1.4 (0.1)15/15
MEMPSODE voglis noiseless 5.2 (5)5.4 (3)4.8 (3)4.3 (3)4.2 (3)10 (8)435 (492)5/15
MLSL pal noiseless 0.23 (0.2)0.22 (0.1)0.21 (0.1)0.20 (0.1)0.21 (0.1)10 (17)638 (564)0/15
OQNLP pal noiseless 0.62 (0.5)0.81 (0.9)0.98 (1)1.6 (2)9.2 (13)1e50/15
P-DCN tran noiseless 1e70/15
P-zero tran noiseless 1e70/15
PRCGA sawyerr noiseless 1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 1e70/15
U-zero tran noiseless 1e70/15
fmincon pal noiseless 0.23 (0.3)0.22 (0.2)0.21 (0.2)0.21 (0.2)0.22 (0.1)8.2 (13)626 (710)0/15
fminunc pal noiseless 0.76 (0.2)0.97 (0.5)1.1 (0.5)1.2 (0.6)1.3 (0.5)2.1 (3)189 (204)0/15
lmm-CMA-ES auger noiseless 0.49 (0.1)0.50 (0.1)0.48 (0.1)0.46 (0.1)0.47 (0.1)0.31 (0.0)0.32 (0.0)15/15
simplex pal noiseless 513 (520)2e50/15
tany liao noiseless 1.9 (0.6)2.1 (0.5)2.1 (0.2)2.0 (0.1)2.0 (0.1)1.3 (0.1)1.3 (0.1)15/15
texp liao noiseless 2.1 (0.7)2.1 (0.4)2.1 (0.1)2.0 (0.3)2.0 (0.2)1.3 (0.1)1.3 (0.1)15/15

Δ fopt
f11, 10-D
1e1
266
1e0
1041
1e-1
2602
1e-2
2954
1e-3
3338
1e-5
4092
1e-7
4843
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 7.2 (0.8)2.1 (0.2)0.95 (0.1)0.89 (0.1)0.84 (0.1)0.76 (0.0)0.71 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 2.3 (0.2)0.63 (0.0)0.27 (0.0)0.25 (0.0)0.23 (0.0)0.21 (0.0)★30.19 (0.0)★315/15
CGA-grid100 holtschulte noiseless 5e50/15
CGA-grid16 holtschulte noiseless 3457 (2588)5e50/15
CGA-ring100 holtschulte noiseless 889 (740)5e50/15
CGA-ring16 holtschulte noiseless 661 (818)7172 (3602)5e50/15
CMAES Hutter hutter noiseless 10020/15
DE Pal pal noiseless 251 (63)702 (587)2e50/15
GA-100 holtschulte noiseless 366 (399)1324 (1275)2829 (1585)5e50/15
HCMA loshchilov noiseless 2.8 (0.3)0.76 (0.1)0.32 (0.0)0.29 (0.0)0.27 (0.0)0.24 (0.0)0.22 (0.0)15/15
HILL holtschulte noiseless 554 (218)2317 (4409)5e50/15
HMLSL pal noiseless 0.27 (0.0)0.09 (0.0)0.05 (1e-2)0.05 (0.0)2.5 (4)216 (233)2e50/15
IP-10DDr liao noiseless 13 (2)4.0 (0.3)1.7 (0.1)1.6 (0.1)1.5 (0.1)1.3 (0.1)1.2 (0.0)15/15
IP-500 liao noiseless 13 (2)4.0 (0.3)1.7 (0.1)1.6 (0.1)1.5 (0.1)1.3 (0.1)1.2 (0.1)15/15
IPOP400D auger noiseless 13 (1)3.8 (0.2)1.7 (0.2)2.1 (0.8)3.0 (2)8.8 (19)48030/15
IP liao noiseless 13 (2)4.0 (0.5)1.7 (0.1)1.6 (0.1)1.5 (0.1)1.3 (0.0)1.2 (0.0)15/15
MEMPSODE voglis noiseless 0.48 (0.0)0.15 (0.0)0.07 (0.0)0.08 (0.1)0.88 (3)17 (13)926 (1265)1/15
MLSL pal noiseless 0.27 (0.0)0.09 (0.0)0.05 (8e-3)0.05 (0.0)2.3 (3)219 (301)2e50/15
OQNLP pal noiseless 0.62 (1)0.50 (0.2)0.85 (0.5)1.6 (2)12 (15)7e40/15
P-DCN tran noiseless 1035 (640)597 (278)332 (176)430 (291)831 (332)1e70/15
P-zero tran noiseless 1441 (1631)849 (755)518 (456)679 (458)1336 (1222)1e70/15
PRCGA sawyerr noiseless 4.6e4 (6e4)9e50/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 880 (609)2253 (1718)1.4e4 (1e4)1e70/15
U-zero tran noiseless 816 (603)4288 (4513)1e70/15
fmincon pal noiseless 0.27 (0.0)0.09 (0.0)0.05 (7e-3)0.05 (0.0)4.4 (8)132 (91)2e50/15
fminunc pal noiseless 1.0 (0.2)1.3 (1)1.6 (3)4.6 (3)60 (63)2e50/15
lmm-CMA-ES auger noiseless 2.9 (0.5)0.85 (0.1)0.38 (0.1)0.36 (0.0)0.33 (0.0)0.30 (0.0)0.27 (0.0)15/15
simplex pal noiseless 332 (182)2e50/15
tany liao noiseless 13 (2)4.0 (0.3)1.7 (0.1)1.6 (0.1)1.5 (0.1)1.3 (0.1)1.2 (0.1)15/15
texp liao noiseless 11 (1)3.3 (0.2)1.5 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.1)1.0 (0.1)15/15

Δ fopt
f12, 10-D
1e1
515
1e0
896
1e-1
1240
1e-2
1390
1e-3
1569
1e-5
3660
1e-7
5154
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.5 (1)3.5 (3)4.1 (0.8)4.3 (2)4.4 (2)2.4 (0.8)2.0 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 1.0 (1)0.85 (0.5)0.96 (0.6)1.1 (0.7)1.2 (0.4)0.74 (0.1)0.63 (0.2)15/15
CGA-grid100 holtschulte noiseless 5e50/15
CGA-grid16 holtschulte noiseless 1078 (1720)5e50/15
CGA-ring100 holtschulte noiseless 508 (179)2049 (1957)5e50/15
CGA-ring16 holtschulte noiseless 331 (1018)973 (404)5850 (7460)5e50/15
CMAES Hutter hutter noiseless 5.7 (6)10020/15
DE Pal pal noiseless 116 (55)374 (394)2e50/15
GA-100 holtschulte noiseless 463 (135)1214 (2670)6021 (5645)5e50/15
HCMA loshchilov noiseless 1.3 (0.2)1.1 (0.5)1.1 (0.6)1.2 (0.8)1.3 (0.7)0.76 (0.2)0.64 (0.3)15/15
HILL holtschulte noiseless 477 (512)1757 (3072)5e50/15
HMLSL pal noiseless 0.71 (0.4)0.75 (0.5)0.80 (0.3)0.80 (0.4)0.80 (0.3)20 (28)45 (39)3/15
IP-10DDr liao noiseless 4.6 (4)5.6 (6)6.2 (5)6.5 (4)6.6 (3)3.5 (2)2.8 (1)15/15
IP-500 liao noiseless 4.6 (5)5.6 (5)6.2 (3)6.5 (4)6.6 (4)3.5 (2)2.8 (1.0)15/15
IPOP400D auger noiseless 3.3 (3)7.3 (14)10 (4)12 (9)15 (12)20 (25)48030/15
IP liao noiseless 4.6 (5)5.6 (4)6.2 (2)6.5 (4)6.6 (4)3.5 (2)2.8 (1.0)15/15
MEMPSODE voglis noiseless 2.6 (2)3.3 (2)3.6 (3)4.6 (2)7.4 (13)8.9 (9)68 (70)11/15
MLSL pal noiseless 0.71 (0.4)0.75 (0.5)0.80 (0.3)0.80 (0.3)0.80 (0.2)0.80 (0.5)9.2 (11)8/15
OQNLP pal noiseless 0.82 (0.4)1.5 (2)6.0 (0.9)8.4 (23)20 (12)60 (66)1e50/15
P-DCN tran noiseless 7079 (1e4)3.1e4 (2e4)1.1e5 (1e5)1.0e5 (1e5)1e70/15
P-zero tran noiseless 4864 (1)3.1e4 (8e4)3.2e4 (5e4)1.0e5 (8e4)1e70/15
PRCGA sawyerr noiseless 249 (282)789 (1513)1178 (2591)4426 (4497)1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 7174 (9705)3.1e4 (4e4)1.1e5 (1e5)1e70/15
U-zero tran noiseless 1.7e4 (2e4)4.5e4 (3e4)5.4e4 (8e4)1e70/15
fmincon pal noiseless 0.72 (0.4)0.73 (0.4)0.80 (0.4)0.79 (0.3)0.79 (0.3)0.97 (2)3.3 (5)8/15
fminunc pal noiseless 0.40 (0.2)0.39 (0.2)0.62 (0.3)0.68 (0.3)0.71 (0.2)1.8 (0.3)17 (21)5/15
lmm-CMA-ES auger noiseless 0.86 (0.1)1.0 (1)1.3 (0.8)1.5 (1)1.7 (0.8)1.1 (0.5)1.1 (0.6)10/15
simplex pal noiseless 16 (32)34 (34)54 (73)156 (164)422 (447)2e50/15
tany liao noiseless 3.1 (2)3.9 (2)4.4 (3)4.9 (1)5.1 (1)2.8 (1.0)2.3 (0.5)15/15
texp liao noiseless 2.5 (0.1)3.4 (1)4.7 (2)5.1 (3)5.4 (2)3.0 (0.8)2.5 (0.8)15/15

Δ fopt
f13, 10-D
1e1
387
1e0
596
1e-1
797
1e-2
1014
1e-3
4587
1e-5
6208
1e-7
7779
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.7 (0.3)3.9 (2)4.3 (2)4.1 (2)1.1 (0.2)1.1 (0.3)1.3 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 0.80 (0.2)0.73 (0.1)0.79 (0.1)0.72 (0.2)0.18 (0.0)0.17 (0.0)0.17 (0.0)15/15
CGA-grid100 holtschulte noiseless 3109 (4111)5e50/15
CGA-grid16 holtschulte noiseless 1594 (2605)5e50/15
CGA-ring100 holtschulte noiseless 180 (61)1026 (610)5e50/15
CGA-ring16 holtschulte noiseless 1244 (984)3663 (5919)5e50/15
CMAES Hutter hutter noiseless 2.2 (0.3)12 (15)10020/15
DE Pal pal noiseless 22 (5)77 (36)422 (214)2e50/15
GA-100 holtschulte noiseless 192 (378)2589 (3146)5e50/15
HCMA loshchilov noiseless 1.1 (0.1)0.89 (0.2)0.84 (0.1)0.76 (0.1)0.21 (0.0)0.20 (0.0)0.19 (0.0)15/15
HILL holtschulte noiseless 940 (2061)2572 (1279)5e50/15
HMLSL pal noiseless 0.75 (0.1)0.73 (0.1)0.72 (0.1)0.70 (0.0)8.4 (12)482 (725)2e50/15
IP-10DDr liao noiseless 2.8 (2)4.4 (5)7.4 (6)7.0 (4)1.9 (0.7)1.9 (0.5)1.9 (0.4)15/15
IP-500 liao noiseless 2.8 (4)4.4 (1)7.4 (5)7.0 (3)1.9 (0.7)1.9 (0.7)1.9 (0.8)15/15
IPOP400D auger noiseless 2.9 (3)5.3 (3)6.4 (2)6.1 (3)3.0 (1)48030/15
IP liao noiseless 2.8 (2)4.4 (7)7.4 (5)7.0 (4)1.9 (0.9)1.9 (0.5)1.9 (0.1)15/15
MEMPSODE voglis noiseless 1.1 (0.1)1.5 (3)1.3 (4)1.3 (0.1)1.4 (1)7.2 (5)50 (122)15/15
MLSL pal noiseless 0.75 (0.1)0.73 (0.0)0.72 (0.1)0.70 (0.1)0.68 (0.9)49 (82)2e50/15
OQNLP pal noiseless 0.74 (0.1)0.69 (0.2)0.62 (0.1)2.0 (1)10 (18)9e40/15
P-DCN tran noiseless 1.3e4 (1e4)4.6e4 (5e4)5.0e4 (7e4)1.4e5 (7e4)3.1e4 (6e4)1e70/15
P-zero tran noiseless 5.2e4 (4e4)2.3e5 (2e5)1e70/15
PRCGA sawyerr noiseless 586 (1310)4326 (6995)7841 (1e4)1.3e4 (1e4)2846 (4889)1e60/15
SMAC-BBOB hutter noiseless 2.2 (3)10000/15
U-DCN tran noiseless 3.0e4 (5e4)6.7e4 (9e4)1.8e5 (3e5)1e70/15
U-zero tran noiseless 3.0e4 (5e4)1.1e5 (2e5)1e70/15
fmincon pal noiseless 0.76 (0.1)0.73 (0.1)0.73 (0.1)0.71 (0.0)0.60 (0.5)58 (63)2e50/15
fminunc pal noiseless 0.90 (0.2)0.99 (0.1)1.00 (0.0)0.98 (0.0)44 (137)485 (381)2e50/15
lmm-CMA-ES auger noiseless 1.1 (0.1)1.3 (0.4)1.4 (0.4)1.2 (0.2)0.32 (0.0)0.32 (0.1)0.32 (0.0)14/15
simplex pal noiseless 25 (59)62 (92)108 (125)693 (350)2e50/15
tany liao noiseless 3.0 (2)6.9 (2)6.2 (1)5.8 (3)1.4 (0.6)1.8 (0.8)2.0 (1.0)15/15
texp liao noiseless 3.3 (2)5.2 (3)6.8 (2)5.8 (4)1.5 (0.8)1.6 (0.5)1.7 (0.4)15/15

Δ fopt
f14, 10-D
1e1
37
1e0
98
1e-1
133
1e-2
205
1e-3
392
1e-5
687
1e-7
4305
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.8 (2)3.5 (0.8)4.1 (0.7)4.3 (0.6)3.5 (0.5)3.7 (0.3)0.89 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 2.0 (2)2.3 (0.3)2.8 (1)2.6 (0.5)1.8 (0.4)1.6 (0.3)0.33 (0.0)15/15
CGA-grid100 holtschulte noiseless 23 (30)90 (39)166 (58)2647 (1602)5e50/15
CGA-grid16 holtschulte noiseless 5.5 (2)14 (6)33 (6)950 (1103)5e50/15
CGA-ring100 holtschulte noiseless 13 (10)55 (7)105 (14)306 (112)5e50/15
CGA-ring16 holtschulte noiseless 5.2 (5)11 (3)21 (7)263 (424)5e50/15
CMAES Hutter hutter noiseless 2.2 (1)2.8 (0.8)3.3 (0.6)3.5 (0.7)19 (27)10020/15
DE Pal pal noiseless 4.7 (3)13 (2)19 (1)24 (3)49 (20)2e50/15
GA-100 holtschulte noiseless 9.4 (6)23 (4)40 (10)245 (161)5e50/15
HCMA loshchilov noiseless 1.0 (0.7)2.4 (2)3.1 (0.9)3.5 (0.8)2.2 (0.4)1.8 (0.4)0.38 (0.1)15/15
HILL holtschulte noiseless 2.7 (1)3.5 (0.8)8.7 (3)201 (175)5e50/15
HMLSL pal noiseless 0.60 (0.1)0.52 (0.1)0.64 (0.2)0.72 (0.1)0.59 (0.1)0.62 (0.1)2e50/15
IP-10DDr liao noiseless 2.5 (2)3.0 (0.5)3.8 (0.3)3.9 (0.6)3.9 (0.5)5.5 (0.5)1.4 (0.1)15/15
IP-500 liao noiseless 2.5 (0.8)3.0 (0.4)3.8 (0.4)3.9 (0.6)3.9 (0.8)5.5 (0.5)1.4 (0.1)15/15
IPOP400D auger noiseless 0.97 (0.6)2.3 (0.3)3.3 (0.5)3.6 (0.5)3.7 (0.6)4.8 (0.6)48030/15
IP liao noiseless 2.5 (2)3.0 (0.6)3.8 (0.5)3.9 (0.6)3.9 (0.6)5.5 (0.5)1.4 (0.1)15/15
MEMPSODE voglis noiseless 2.5 (0.6)1.5 (0.2)1.3 (0.2)1.1 (0.1)0.72 (0.1)0.57 (0.1)71 (159)13/15
MLSL pal noiseless 0.60 (0.3)0.52 (0.1)0.64 (0.1)0.72 (0.1)0.59 (0.1)0.62 (0.1)644 (843)0/15
OQNLP pal noiseless 0.99 (0.3)0.82 (0.2)0.88 (0.2)0.82 (0.1)0.57 (0.1)90 (97)3e40/15
P-DCN tran noiseless 6.9 (8)15 (5)14 (4)19 (10)470 (174)1e70/15
P-zero tran noiseless 7.5 (8)13 (6)12 (2)14 (6)1086 (625)1e70/15
PRCGA sawyerr noiseless 4.4 (3)14 (5)20 (6)31 (32)2190 (3689)1e60/15
SMAC-BBOB hutter noiseless 1.4 (2)29 (42)10000/15
U-DCN tran noiseless 2.9 (2)12 (3)30 (15)146 (84)1089 (539)1e70/15
U-zero tran noiseless 2.5 (0.8)6.7 (2)18 (6)452 (230)1e70/15
fmincon pal noiseless 0.60 (0.2)0.52 (0.1)0.64 (0.2)0.72 (0.2)0.59 (0.2)0.61 (0.0)650 (503)0/15
fminunc pal noiseless 0.68 (0.3)1.1 (0.4)1.3 (0.3)1.2 (0.4)0.86 (0.2)0.82 (0.2)2e50/15
lmm-CMA-ES auger noiseless 0.93 (0.6)1.9 (0.3)2.1 (0.4)2.1 (0.3)1.7 (0.3)1.7 (0.2)0.40 (0.0)15/15
simplex pal noiseless 20 (16)32 (38)48 (31)228 (170)545 (951)2e50/15
tany liao noiseless 1.7 (0.9)2.9 (0.6)3.7 (1.0)4.1 (0.9)3.9 (0.7)5.4 (0.5)1.4 (0.1)15/15
texp liao noiseless 1.3 (1)2.7 (0.5)3.7 (0.4)3.9 (0.4)3.8 (0.6)4.8 (0.4)1.3 (0.1)15/15

Δ fopt
f15, 10-D
1e1
4774
1e0
39246
1e-1
73643
1e-2
74669
1e-3
75790
1e-5
77814
1e-7
79834
#succ
12/15
BIPOP-aCMA-STEP loshchilov noiseless 1.0 (0.5)1.4 (1)1.1 (1)1.1 (0.3)1.1 (0.4)1.1 (0.7)1.1 (0.9)15/15
BIPOP-saACM-k loshchilov noiseless 1.1 (0.5)1.0 (0.2)0.81 (0.3)0.80 (0.4)0.79 (0.3)0.77 (0.3)0.78 (0.3)15/15
CGA-grid100 holtschulte noiseless 5e50/15
CGA-grid16 holtschulte noiseless 1534 (943)5e50/15
CGA-ring100 holtschulte noiseless 97 (209)5e50/15
CGA-ring16 holtschulte noiseless 1468 (1545)5e50/15
CMAES Hutter hutter noiseless 3.1 (3)10020/15
DE Pal pal noiseless 618 (482)2e50/15
GA-100 holtschulte noiseless 177 (274)5e50/15
HCMA loshchilov noiseless 0.73 (0.7)1.3 (0.4)0.96 (0.5)0.95 (0.3)0.93 (0.4)0.94 (0.5)0.92 (0.3)15/15
HILL holtschulte noiseless 1483 (1414)5e50/15
HMLSL pal noiseless 12 (11)2e50/15
IP-10DDr liao noiseless 1.1 (0.7)1.2 (0.7)0.90 (0.2)0.91 (0.2)0.91 (0.2)0.92 (0.3)0.93 (0.3)15/15
IP-500 liao noiseless 1.1 (0.6)1.2 (0.5)0.90 (0.5)0.90 (0.5)0.90 (0.2)0.91 (0.5)0.92 (0.6)15/15
IPOP400D auger noiseless 2.3 (2)48150/15
IP liao noiseless 1.1 (0.4)1.2 (0.6)0.90 (0.4)0.91 (0.2)0.91 (0.4)0.92 (0.2)0.93 (0.2)15/15
MEMPSODE voglis noiseless 13 (4)25 (13)54 (79)53 (95)52 (49)51 (31)50 (51)11/15
MLSL pal noiseless 2e50/15
OQNLP pal noiseless 95 (138)7e40/15
P-DCN tran noiseless 1e70/15
P-zero tran noiseless 1e70/15
PRCGA sawyerr noiseless 50 (228)1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 1e70/15
U-zero tran noiseless 1e70/15
fmincon pal noiseless 558 (548)2e50/15
fminunc pal noiseless 2e50/15
lmm-CMA-ES auger noiseless 0.47 (0.3)48170/15
simplex pal noiseless 2e50/15
tany liao noiseless 0.80 (0.5)0.98 (0.6)0.88 (0.4)0.88 (0.4)0.89 (0.3)0.90 (0.3)0.90 (0.5)15/15
texp liao noiseless 0.90 (0.6)1.0 (1)0.87 (0.4)0.88 (0.5)0.90 (0.5)0.92 (0.5)0.95 (0.5)15/15

Δ fopt
f16, 10-D
1e1
425
1e0
7029
1e-1
15779
1e-2
45669
1e-3
51151
1e-5
65798
1e-7
71570
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.8 (1)1.0 (0.8)1.1 (0.4)0.66 (0.5)0.75 (0.5)0.61 (0.3)0.57 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (0.9)0.81 (0.6)0.74 (1.0)0.50 (0.2)0.58 (0.5)0.51 (0.4)0.56 (0.2)15/15
CGA-grid100 holtschulte noiseless 13 (20)1054 (1174)5e50/15
CGA-grid16 holtschulte noiseless 13 (2)5e50/15
CGA-ring100 holtschulte noiseless 8.6 (5)66 (102)463 (832)5e50/15
CGA-ring16 holtschulte noiseless 4.0 (3)998 (1423)5e50/15
CMAES Hutter hutter noiseless 3.7 (4)1.0 (0.9)10020/15
DE Pal pal noiseless 33 (20)2e50/15
GA-100 holtschulte noiseless 14 (7)95 (154)5e50/15
HCMA loshchilov noiseless 2.7 (1.0)0.94 (0.6)0.84 (0.3)0.39 (0.2)0.39 (0.2)0.39 (0.2)0.44 (0.2)15/15
HILL holtschulte noiseless 52 (190)1033 (1103)5e50/15
HMLSL pal noiseless 16 (8)2e50/15
IP-10DDr liao noiseless 1.8 (0.3)0.33 (0.4)0.69 (0.6)0.75 (0.6)0.85 (0.2)0.74 (0.4)0.73 (0.3)15/15
IP-500 liao noiseless 1.8 (0.6)0.33 (0.3)0.69 (0.6)0.75 (1)0.85 (0.5)0.74 (0.5)0.73 (0.6)15/15
IPOP400D auger noiseless 2.3 (0.8)2.1 (0.9)48030/15
IP liao noiseless 1.8 (0.5)0.33 (0.5)0.69 (0.6)0.75 (0.4)0.85 (0.5)0.74 (0.7)0.73 (0.3)15/15
MEMPSODE voglis noiseless 7.6 (13)44 (46)139 (222)77 (28)146 (161)175 (114)483 (385)0/15
MLSL pal noiseless 32 (16)2e50/15
OQNLP pal noiseless 59 (32)8e40/15
P-DCN tran noiseless 1.0 (0.6)2.0e4 (2e4)1e70/15
P-zero tran noiseless 5901 (1e4)1e70/15
PRCGA sawyerr noiseless 10 (7)173 (178)1e60/15
SMAC-BBOB hutter noiseless 1.2 (1)10000/15
U-DCN tran noiseless 4.7 (7)3376 (2957)1e70/15
U-zero tran noiseless 4.9 (5)3134 (5723)1e70/15
fmincon pal noiseless 17 (7)2e50/15
fminunc pal noiseless 294 (289)2e50/15
lmm-CMA-ES auger noiseless 1.3 (0.7)0.53 (1.0)0.80 (0.8)1.6 (2)48050/15
simplex pal noiseless 9.1 (12)2e50/15
tany liao noiseless 2.1 (0.7)0.46 (0.4)0.71 (0.4)0.48 (0.3)0.61 (0.4)0.59 (0.4)0.57 (0.3)15/15
texp liao noiseless 1.4 (1)0.40 (0.5)0.46 (0.4)0.54 (0.6)0.56 (0.6)0.49 (0.5)0.48 (0.7)15/15

Δ fopt
f17, 10-D
1e1
26
1e0
429
1e-1
2203
1e-2
6329
1e-3
9851
1e-5
20190
1e-7
26503
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.5 (3)1.2 (0.4)1.1 (1)0.74 (0.8)1.2 (0.4)1.2 (0.7)1.4 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 2.8 (1)1.2 (0.4)0.58 (0.1)1.2 (0.7)1.2 (0.5)1.7 (0.7)2.8 (2)15/15
CGA-grid100 holtschulte noiseless 4.0 (6)4930 (4993)5e50/15
CGA-grid16 holtschulte noiseless 3.2 (4)975 (1533)5e50/15
CGA-ring100 holtschulte noiseless 6.3 (8)38 (17)3296 (2837)5e50/15
CGA-ring16 holtschulte noiseless 3.1 (3)307 (306)5e50/15
CMAES Hutter hutter noiseless 2.2 (2)1.2 (0.8)0.55 (0.2)10020/15
DE Pal pal noiseless 3.0 (4)6.9 (0.7)5.4 (1)4.0 (0.8)4.8 (5)5.1 (4)8.0 (4)10/15
GA-100 holtschulte noiseless 4.4 (3)8.3 (2)651 (468)5e50/15
HCMA loshchilov noiseless 2.2 (1)1.5 (0.9)1.2 (0.1)1.0 (0.7)1.3 (0.6)1.4 (0.9)2.8 (0.7)15/15
HILL holtschulte noiseless 32 (5)2531 (2622)5e50/15
HMLSL pal noiseless 18 (17)10 (4)7.5 (2)5.7 (1)6.0 (2)6.5 (2)8.7 (4)10/15
IP-10DDr liao noiseless 1.5 (1)1.1 (0.4)0.71 (1)1.3 (2)1.1 (1)1.1 (0.3)1.2 (0.5)15/15
IP-500 liao noiseless 1.5 (0.7)1.1 (0.4)0.71 (1)1.3 (2)1.1 (0.6)1.1 (0.5)1.2 (0.5)15/15
IPOP400D auger noiseless 0.64 (0.6)0.99 (0.2)1.5 (2)0.72 (0.8)2.1 (2)48030/15
IP liao noiseless 1.5 (1)1.1 (0.2)0.71 (0.2)1.3 (3)1.1 (2)1.1 (0.5)1.2 (1)15/15
MEMPSODE voglis noiseless 25 (70)99 (39)488 (608)579 (990)503 (1154)566 (748)5e60/15
MLSL pal noiseless 17 (43)2e50/15
OQNLP pal noiseless 10 (7)1e50/15
P-DCN tran noiseless 1.6 (1)1e70/15
P-zero tran noiseless 1.8 (0.8)1e70/15
PRCGA sawyerr noiseless 2.2 (2)5.0 (2)125 (349)114 (86)201 (326)6e50/15
SMAC-BBOB hutter noiseless 0.80 (0.5)10000/15
U-DCN tran noiseless 1.9 (1)9349 (3307)1e70/15
U-zero tran noiseless 1.5 (0.8)1.8e4 (1e4)6.6e4 (7e4)1e70/15
fmincon pal noiseless 20 (12)2e50/15
fminunc pal noiseless 15 (14)2e50/15
lmm-CMA-ES auger noiseless 0.64 (0.7)0.75 (0.4)0.55 (1)0.83 (1.0)6.9 (7)48100/15
simplex pal noiseless 34 (29)2e50/15
tany liao noiseless 1.6 (1)1.1 (0.3)0.85 (0.8)0.52 (0.5)0.75 (0.8)0.77 (0.3)0.84 (0.4)15/15
texp liao noiseless 1.8 (1)1.2 (0.7)1.1 (0.2)1.1 (1)0.99 (0.5)0.73 (0.1)0.90 (0.4)15/15

Δ fopt
f18, 10-D
1e1
238
1e0
836
1e-1
7012
1e-2
15928
1e-3
27536
1e-5
37234
1e-7
42708
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.4 (0.5)2.5 (4)1.1 (1.0)0.96 (0.4)0.97 (0.4)0.98 (0.4)1.1 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 1.2 (0.4)2.9 (6)0.97 (0.9)0.84 (0.3)0.74 (0.4)1.0 (0.3)1.6 (1)15/15
CGA-grid100 holtschulte noiseless 59 (76)5e50/15
CGA-grid16 holtschulte noiseless 724 (1066)8406 (6878)5e50/15
CGA-ring100 holtschulte noiseless 16 (3)531 (598)5e50/15
CGA-ring16 holtschulte noiseless 4.3 (2)2406 (2994)5e50/15
CMAES Hutter hutter noiseless 1.2 (0.5)1.7 (1)10020/15
DE Pal pal noiseless 4.8 (1)13 (10)7.8 (8)15 (13)34 (30)2e50/15
GA-100 holtschulte noiseless 6.8 (2)179 (301)5e50/15
HCMA loshchilov noiseless 1.7 (0.4)3.9 (6)1.1 (0.7)0.74 (0.4)0.52 (0.2)1.1 (0.5)1.4 (1)15/15
HILL holtschulte noiseless 439 (128)5e50/15
HMLSL pal noiseless 12 (5)21 (9)11 (8)33 (29)107 (154)2e50/15
IP-10DDr liao noiseless 0.96 (0.2)0.87 (0.1)0.51 (0.6)0.87 (0.6)0.94 (0.4)0.99 (0.3)1.00 (0.2)15/15
IP-500 liao noiseless 0.96 (0.3)0.87 (0.2)0.51 (0.5)0.87 (0.8)0.94 (0.4)0.99 (0.2)1.00 (0.2)15/15
IPOP400D auger noiseless 0.88 (0.3)1.8 (3)0.96 (2)4.3 (3)48030/15
IP liao noiseless 0.96 (0.3)0.87 (0.2)0.51 (0.3)0.87 (0.6)0.94 (0.4)0.99 (0.2)1.00 (0.0)15/15
MEMPSODE voglis noiseless 74 (25)521 (194)652 (1581)771 (405)824 (1626)5e60/15
MLSL pal noiseless 307 (297)2e50/15
OQNLP pal noiseless 186 (227)1e50/15
P-DCN tran noiseless 5.1e4 (9e4)1e70/15
P-zero tran noiseless 1.7e5 (2e5)1e70/15
PRCGA sawyerr noiseless 4.2 (1)56 (101)100 (160)582 (734)5e50/15
SMAC-BBOB hutter noiseless 5.4 (5)10000/15
U-DCN tran noiseless 7.6 (10)1e70/15
U-zero tran noiseless 3778 (1e4)1e70/15
fmincon pal noiseless 270 (246)2e50/15
fminunc pal noiseless 242 (167)2e50/15
lmm-CMA-ES auger noiseless 0.70 (0.2)0.63 (0.2)0.86 (0.7)4.3 (2)48080/15
simplex pal noiseless 725 (878)2e50/15
tany liao noiseless 1.1 (0.4)1.4 (2)0.40 (1)0.64 (0.3)0.64 (0.6)0.93 (0.0)0.94 (0.0)15/15
texp liao noiseless 1.2 (0.4)3.7 (5)0.98 (1)1.1 (0.6)0.86 (0.3)0.77 (0.3)0.79 (0.2)15/15

Δ fopt
f19, 10-D
1e1
1
1e0
1
1e-1
10609
1e-2
9.8e5
1e-3
1.4e6
1e-5
1.4e6
1e-7
1.4e6
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 104 (44)8407 (8070)7.5 (9)1.0 (0.4)0.98 (0.3)0.98 (0.4)0.98 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 53 (22)8766 (2966)8.2 (5)0.59 (0.3)0.61 (0.5)0.61 (0.4)0.61 (0.3)15/15
CGA-grid100 holtschulte noiseless 683 (442)3.5e6 (4e6)5e50/15
CGA-grid16 holtschulte noiseless 194 (190)2.3e6 (2e6)5e50/15
CGA-ring100 holtschulte noiseless 599 (306)4.3e5 (3e5)5e50/15
CGA-ring16 holtschulte noiseless 174 (103)9.6e5 (9e5)5e50/15
CMAES Hutter hutter noiseless 59 (43)10020/15
DE Pal pal noiseless 202 (177)2.9e6 (4e6)2e50/15
GA-100 holtschulte noiseless 338 (303)6.3e5 (8e5)5e50/15
HCMA loshchilov noiseless 24 (2)1.0e4 (8936)7.9 (5)0.69 (0.5)0.63 (0.3)0.63 (0.3)0.63 (0.3)15/15
HILL holtschulte noiseless 111 (124)1.2e6 (2e6)5e50/15
HMLSL pal noiseless 1 (0)1 (0)7.7e-3 (5e-5)2e50/15
IP-10DDr liao noiseless 47 (50)7.8e4 (2e5)67 (88)2.7 (3)4.5 (6)4.4 (4)4.4 (6)13/15
IP-500 liao noiseless 47 (45)7.8e4 (2e5)67 (90)2.8 (3)3.1 (2)3.0 (5)3.0 (2)14/15
IPOP400D auger noiseless 1 (0)1 (0)48050/15
IP liao noiseless 47 (45)7.8e4 (1e5)67 (83)1.3 (0.7)1.0 (0.5)1.0 (0.4)1.0 (0.6)15/15
MEMPSODE voglis noiseless 964 (1850)2.5e4 (1e4)36 (14)73 (98)5e60/15
MLSL pal noiseless 1 (0)1 (0)7.7e-3 (5e-5)2e50/15
OQNLP pal noiseless 1 (0)1 (0)4.8e-3 (5e-5)★46e40/15
P-DCN tran noiseless 208 (228)1.5e8 (4e8)1e70/15
P-zero tran noiseless 7.7e5 (2e5)1e70/15
PRCGA sawyerr noiseless 93 (44)759 (205)0.61 (0.2)6e50/15
SMAC-BBOB hutter noiseless 1 (0)1 (0)10000/15
U-DCN tran noiseless 113 (125)1.2e7 (1e7)1e70/15
U-zero tran noiseless 105 (48)8.0e6 (9e6)1e70/15
fmincon pal noiseless 1 (0)1 (0)7.7e-3 (5e-5)2e50/15
fminunc pal noiseless 1 (0)1 (0)8.0e-3 (5e-4)2e50/15
lmm-CMA-ES auger noiseless 1 (0)1 (0)48050/15
simplex pal noiseless 1 (0)1 (0)0.02 (6e-3)2e50/15
tany liao noiseless 32 (32)8111 (4261)34 (41)1.7 (1)2.6 (2)2.6 (2)2.6 (2)15/15
texp liao noiseless 4.0 (2)9109 (7502)19 (8)1.5 (1)1.8 (1)1.8 (2)1.8 (1)15/15

Δ fopt
f20, 10-D
1e1
32
1e0
15426
1e-1
5.5e5
1e-2
5.7e5
1e-3
5.7e5
1e-5
5.8e5
1e-7
5.9e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 7.9 (1)3.0 (2)1.2 (0.7)1.2 (0.7)1.2 (0.7)1.2 (0.7)1.2 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 4.2 (0.3)1.0 (1)1.1 (0.3)1.1 (0.7)1.1 (0.4)1.1 (0.6)1.1 (0.4)15/15
CGA-grid100 holtschulte noiseless 125 (46)3.9 (4)13 (39)13 (23)5e50/15
CGA-grid16 holtschulte noiseless 24 (10)0.50 (0.6)5e50/15
CGA-ring100 holtschulte noiseless 61 (14)0.92 (0.1)0.44 (0.7)0.47 (0.5)0.56 (0.3)13 (21)5e50/15
CGA-ring16 holtschulte noiseless 16 (3)0.25 (0.1)5e50/15
CMAES Hutter hutter noiseless 5.1 (2)0.97 (0.6)10020/15
DE Pal pal noiseless 17 (7)0.75 (0.2)2.4 (5)2.3 (2)2.3 (4)2.3 (3)2.2 (2)2/15
GA-100 holtschulte noiseless 37 (10)0.55 (0.1)6.0 (3)5.8 (6)5.9 (4)13 (18)5e50/15
HCMA loshchilov noiseless 0.90 (0.2)0.87 (0.6)1.1 (0.7)1.1 (0.6)1.1 (0.4)1.1 (0.7)1.1 (0.5)15/15
HILL holtschulte noiseless 5.3 (3)0.22 (0.1)14 (8)13 (14)5e50/15
HMLSL pal noiseless 1.6 (0)0.57 (0.4)0.80 (0.6)0.77 (1)0.77 (1)0.76 (0.2)0.75 (0.3)5/15
IP-10DDr liao noiseless 6.2 (0.8)3.0 (2)8.1 (13)7.9 (5)7.8 (6)7.7 (9)7.6 (15)13/15
IP-500 liao noiseless 6.2 (1)3.0 (1)6.8 (12)6.6 (6)6.6 (6)6.5 (8)6.4 (8)14/15
IPOP400D auger noiseless 3.5 (1)48050/15
IP liao noiseless 6.2 (1)3.0 (2)0.85 (0.6)0.86 (0.5)0.87 (0.6)0.88 (0.6)0.88 (0.3)15/15
MEMPSODE voglis noiseless 3.8 (0.4)1.1 (1)3.2 (3)3.6 (3)3.5 (3)3.5 (3)3.4 (2)14/15
MLSL pal noiseless 1.6 (0)1.3 (0.6)2e50/15
OQNLP pal noiseless 0.91 (0)8.7 (4)4e40/15
P-DCN tran noiseless 20 (13)15 (20)1e70/15
P-zero tran noiseless 21 (11)25 (22)1e70/15
PRCGA sawyerr noiseless 10 (3)14 (28)9e50/15
SMAC-BBOB hutter noiseless 1.2 (0.4)10000/15
U-DCN tran noiseless 14 (16)1.4 (0.5)122 (107)118 (145)117 (131)115 (83)114 (136)2/15
U-zero tran noiseless 12 (4)1.1 (3)74 (141)72 (123)72 (82)72 (49)77 (186)0/15
fmincon pal noiseless 1.6 (0)1.1 (1)2e50/15
fminunc pal noiseless 1.1 (0)0.87 (0.6)2e50/15
lmm-CMA-ES auger noiseless 3.3 (1)48170/15
simplex pal noiseless 18 (17)4.1 (6)2e50/15
tany liao noiseless 5.7 (1)3.6 (1)2.7 (2)2.6 (2)2.6 (2)2.6 (2)2.5 (7)15/15
texp liao noiseless 2.1 (1)4.9 (3)7.4 (6)7.3 (8)7.2 (3)7.1 (8)7.0 (5)14/15

Δ fopt
f21, 10-D
1e1
130
1e0
2236
1e-1
4392
1e-2
4487
1e-3
4618
1e-5
5074
1e-7
11329
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 11 (25)55 (43)62 (99)60 (132)59 (135)54 (86)24 (52)15/15
BIPOP-saACM-k loshchilov noiseless 2.6 (3)2.9 (3)1.9 (2)1.9 (2)1.8 (1)1.7 (2)0.75 (0.7)15/15
CGA-grid100 holtschulte noiseless 333 (60)399 (769)491 (427)771 (1533)1558 (1868)5e50/15
CGA-grid16 holtschulte noiseless 302 (41)1465 (2233)5e50/15
CGA-ring100 holtschulte noiseless 20 (4)39 (59)32 (142)35 (5)38 (84)49 (53)35 (18)7/15
CGA-ring16 holtschulte noiseless 5.4 (2)454 (443)1595 (2106)1561 (724)1518 (2409)1388 (1601)628 (386)1/15
CMAES Hutter hutter noiseless 3.7 (4)1.4 (2)1.6 (2)1.6 (2)1.6 (2)1.4 (2)0.66 (0.9)0/15
DE Pal pal noiseless 16 (12)136 (202)70 (92)69 (67)67 (44)62 (79)28 (58)6/15
GA-100 holtschulte noiseless 17 (19)337 (727)229 (256)225 (362)220 (459)209 (296)104 (90)5/15
HCMA loshchilov noiseless 1.8 (1)8.7 (2)24 (73)23 (39)22 (38)21 (22)9.3 (4)15/15
HILL holtschulte noiseless 1764 (5349)630 (503)740 (455)725 (669)705 (1218)644 (567)295 (287)2/15
HMLSL pal noiseless 6.8 (11)3.1 (5)2.2 (1)2.1 (2)2.1 (3)1.9 (4)0.91 (1)11/15
IP-10DDr liao noiseless 3.5 (0.4)22 (54)37 (28)36 (17)35 (48)32 (96)15 (24)15/15
IP-500 liao noiseless 3.5 (6)23 (52)108 (103)105 (501)103 (75)94 (44)42 (6)15/15
IPOP400D auger noiseless 2.7 (0.6)3.6 (4)2.3 (4)2.3 (3)2.2 (3)2.1 (5)0.94 (2)5/15
IP liao noiseless 3.5 (0.5)379 (1286)867 (1710)851 (569)828 (632)755 (988)339 (881)11/15
MEMPSODE voglis noiseless 27 (23)24 (50)48 (111)47 (62)46 (61)42 (15)19 (25)15/15
MLSL pal noiseless 2.7 (3)1.2 (2)0.89 (1)0.88 (0.9)0.87 (1)0.82 (1)0.40 (0.2)14/15
OQNLP pal noiseless 3.3 (5)2.2 (3)2.4 (2)2.3 (1)2.3 (2)2.1 (6)10 (13)0/15
P-DCN tran noiseless 2.8e4 (4e4)6.3e4 (1e5)3.2e4 (3e4)3.1e4 (5e4)3.0e4 (4e4)2.8e4 (2e4)1.2e4 (1e4)1/15
P-zero tran noiseless 5.1e4 (2e5)6.3e4 (9e4)3.2e4 (7e4)3.1e4 (4e4)3.0e4 (5e4)2.8e4 (2e4)1.2e4 (1e4)1/15
PRCGA sawyerr noiseless 636 (3852)537 (387)274 (200)268 (384)262 (342)241 (142)112 (148)6/15
SMAC-BBOB hutter noiseless 2.8 (6)1.3 (2)1.6 (2)10000/15
U-DCN tran noiseless 10 (20)1.8e4 (3e4)1.5e4 (9677)1.4e4 (2e4)1.4e4 (2e4)1.3e4 (2e4)5745 (2870)2/15
U-zero tran noiseless 5620 (2e4)6.3e4 (8e4)3.2e4 (6e4)3.1e4 (4e4)3.0e4 (3e4)2.8e4 (3e4)1.2e4 (1e4)1/15
fmincon pal noiseless 2.4 (3)0.98 (1.0)1.0 (2)0.99 (2)0.97 (0.7)0.92 (1)0.44 (0.6)15/15
fminunc pal noiseless 3.7 (3)0.79 (0.8)1.2 (2)1.2 (1)1.2 (2)1.2 (2)1.3 (2)9/15
lmm-CMA-ES auger noiseless 3.2 (6)2.1 (3)1.4 (3)1.4 (0.9)1.4 (1)1.3 (2)0.66 (0.7)7/15
simplex pal noiseless 14 (7)4.6 (3)8.8 (3)11 (8)11 (6)15 (18)8.2 (9)13/15
tany liao noiseless 7.5 (5)19 (18)56 (139)55 (32)54 (11)49 (50)22 (43)15/15
texp liao noiseless 4.0 (6)29 (67)19 (19)19 (34)19 (32)17 (17)7.9 (9)15/15

Δ fopt
f22, 10-D
1e1
98
1e0
2839
1e-1
6353
1e-2
6620
1e-3
6798
1e-5
8296
1e-7
10351
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 44 (77)6.6 (12)155 (97)149 (92)145 (452)119 (312)95 (255)14/15
BIPOP-saACM-k loshchilov noiseless 8.2 (5)6.7 (25)44 (240)42 (231)41 (24)34 (9)27 (7)15/15
CGA-grid100 holtschulte noiseless 675 (3823)238 (211)1114 (1318)5e50/15
CGA-grid16 holtschulte noiseless 2315 (3848)534 (644)1108 (1554)5e50/15
CGA-ring100 holtschulte noiseless 24 (11)4.8 (3)82 (105)154 (191)1080 (736)5e50/15
CGA-ring16 holtschulte noiseless 6.5 (4)89 (88)233 (177)320 (378)493 (580)858 (467)5e50/15
CMAES Hutter hutter noiseless 6.0 (16)0.85 (0.6)10020/15
DE Pal pal noiseless 172 (523)108 (247)448 (480)432 (181)422 (515)349 (506)282 (391)1/15
GA-100 holtschulte noiseless 381 (1277)491 (616)5e50/15
HCMA loshchilov noiseless 6.7 (7)28 (14)53 (149)51 (143)50 (20)41 (10)41 (56)15/15
HILL holtschulte noiseless 1290 (2554)356 (531)331 (531)345 (510)1079 (772)5e50/15
HMLSL pal noiseless 15 (15)6.4 (18)3.0 (8)2.9 (8)2.9 (0.5)2.4 (18)2.0 (5)8/15
IP-10DDr liao noiseless 24 (25)411 (387)1.1e4 (2e4)1.0e4 (8709)1.0e4 (1e4)8271 (6027)6629 (5313)2/15
IP-500 liao noiseless 24 (53)1239 (185)1e70/15
IPOP400D auger noiseless 3.8 (1)1.9 (2)11 (12)10 (6)10 (8)8.3 (4)6.7 (4)1/15
IP liao noiseless 24 (53)2490 (2242)1e70/15
MEMPSODE voglis noiseless 141 (164)21 (20)24 (12)23 (33)22 (22)18 (22)33 (71)15/15
MLSL pal noiseless 5.0 (5)0.51 (0.5)1.0 (0.4)1.0 (2)0.99 (0.8)0.85 (1)0.75 (1)14/15
OQNLP pal noiseless 3.3 (3)2.6 (7)2.8 (1)2.7 (3)2.8 (3)2.3 (7)3e40/15
P-DCN tran noiseless 8.9e4 (1e5)2.3e4 (2e4)2.2e4 (2e4)2.1e4 (6e4)2.1e4 (4e4)1.7e4 (2e4)1.4e4 (2e4)1/15
P-zero tran noiseless 3.7e4 (3e4)1.4e4 (1e4)1.0e4 (1e4)9821 (7175)9567 (1e4)7859 (7838)6361 (9406)2/15
PRCGA sawyerr noiseless 1475 (5106)260 (656)591 (722)574 (1014)577 (668)1578 (2411)1e60/15
SMAC-BBOB hutter noiseless 6.0 (10)5.0 (5)10000/15
U-DCN tran noiseless 24 (86)2406 (4504)3202 (1985)3099 (5359)3049 (3347)2593 (1591)2167 (3140)5/15
U-zero tran noiseless 6181 (1e4)4203 (3522)2386 (2906)2730 (3897)2786 (3953)4163 (7816)1e70/15
fmincon pal noiseless 5.6 (6)0.63 (1)0.69 (0.4)0.66 (0.4)0.66 (0.9)0.58 (0.6)0.54 (0.4)13/15
fminunc pal noiseless 5.0 (5)0.49 (0.4)0.86 (2)0.86 (1)0.87 (1)0.79 (0.5)0.80 (0.3)11/15
lmm-CMA-ES auger noiseless 2.5 (3)1.6 (3)11 (6)10 (6)10 (12)8.3 (6)6.7 (10)1/15
simplex pal noiseless 23 (13)3.8 (4)12 (25)15 (14)16 (8)27 (19)138 (126)1/15
tany liao noiseless 36 (66)378 (228)2997 (2827)2876 (3846)2801 (3746)2295 (1578)1840 (2643)6/15
texp liao noiseless 113 (365)22 (28)99 (86)95 (53)93 (209)76 (50)61 (86)15/15

Δ fopt
f23, 10-D
1e1
3.0
1e0
915
1e-1
16425
1e-2
1.8e5
1e-3
2.0e5
1e-5
2.1e5
1e-7
2.1e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.4 (0.4)20 (9)2.9 (5)1.2 (0.6)1.3 (0.8)1.3 (1)1.3 (2)15/15
BIPOP-saACM-k loshchilov noiseless 2.7 (2)16 (14)1.6 (2)0.31 (0.3)0.35 (0.3)0.45 (0.4)0.63 (0.3)15/15
CGA-grid100 holtschulte noiseless 1.4 (1)207 (171)5e50/15
CGA-grid16 holtschulte noiseless 2.1 (1)113 (53)5e50/15
CGA-ring100 holtschulte noiseless 1.3 (0.9)56 (33)5e50/15
CGA-ring16 holtschulte noiseless 2.1 (2)73 (140)5e50/15
CMAES Hutter hutter noiseless 2.1 (3)10020/15
DE Pal pal noiseless 1.7 (2)256 (67)2e50/15
GA-100 holtschulte noiseless 1.6 (2)161 (237)5e50/15
HCMA loshchilov noiseless 6.2 (4)14 (9)1.5 (2)0.31 (0.1)0.44 (0.5)0.57 (0.8)0.65 (0.6)15/15
HILL holtschulte noiseless 2.2 (3)86 (24)5e50/15
HMLSL pal noiseless 5.8 (5)4.0 (4)32 (15)2e50/15
IP-10DDr liao noiseless 2.0 (2)16 (23)7.1 (7)10 (5)9.3 (14)9.1 (10)8.9 (17)15/15
IP-500 liao noiseless 2.0 (2)16 (18)7.1 (7)13 (18)12 (16)11 (16)11 (16)15/15
IPOP400D auger noiseless 2.0 (4)48150/15
IP liao noiseless 2.0 (2)16 (18)7.1 (7)28 (30)26 (39)25 (24)25 (89)12/15
MEMPSODE voglis noiseless 2.3 (3)11 (7)25 (35)403 (674)5e60/15
MLSL pal noiseless 5.8 (7)2.0 (3)30 (27)2e50/15
OQNLP pal noiseless 11 (12)3.4 (3)33 (55)8e40/15
P-DCN tran noiseless 1.6 (1)11 (4)1e70/15
P-zero tran noiseless 1.9 (2)427 (1583)1e70/15
PRCGA sawyerr noiseless 2.0 (2)438 (403)5e50/15
SMAC-BBOB hutter noiseless 1.7 (0.5)10000/15
U-DCN tran noiseless 2.2 (0.4)116 (394)1e70/15
U-zero tran noiseless 1.9 (2)28 (18)1e70/15
fmincon pal noiseless 7.0 (11)2.6 (2)30 (30)2e50/15
fminunc pal noiseless 8.2 (12)31 (34)2e50/15
lmm-CMA-ES auger noiseless 1.7 (1)38 (38)48090/15
simplex pal noiseless 180 (248)2.9 (0.9)39 (40)2e50/15
tany liao noiseless 1.6 (0.8)24 (25)7.6 (22)14 (10)15 (14)15 (19)15 (13)14/15
texp liao noiseless 1.7 (2)18 (19)18 (36)16 (16)15 (11)14 (12)14 (13)15/15

Δ fopt
f24, 10-D
1e1
98761
1e0
1.0e6
1e-1
7.5e7
1e-2
7.5e7
1e-3
7.5e7
1e-5
7.5e7
1e-7
7.5e7
#succ
1/15
BIPOP-aCMA-STEP loshchilov noiseless 0.95 (0.6)1.1 (2)0.95 (0.8)0.98 (1)0.98 (0.4)0.98 (0.6)0.98 (1)2/15
BIPOP-saACM-k loshchilov noiseless 0.64 (1.0)1.6 (2)0.28 (0.6)0.47 (0.5)0.62 (0.3)0.62 (1.0)0.62 (0.5)3/15
CGA-grid100 holtschulte noiseless 5e50/15
CGA-grid16 holtschulte noiseless 5e50/15
CGA-ring100 holtschulte noiseless 74 (37)5e50/15
CGA-ring16 holtschulte noiseless 71 (56)5e50/15
CMAES Hutter hutter noiseless 10020/15
DE Pal pal noiseless 2e50/15
GA-100 holtschulte noiseless 72 (78)5e50/15
HCMA loshchilov noiseless 1.1 (2)1.3 (1.0)0.19 (0.2)0.27 (0.4)0.27 (0.2)0.34 (0.5)0.34 (0.5)5/15
HILL holtschulte noiseless 5e50/15
HMLSL pal noiseless 14 (15)2e50/15
IP-10DDr liao noiseless 179 (167)1e70/15
IP-500 liao noiseless 1e70/15
IPOP400D auger noiseless 48050/15
IP liao noiseless 1e70/15
MEMPSODE voglis noiseless 77 (127)12 (11)5e60/15
MLSL pal noiseless 2e50/15
OQNLP pal noiseless 0.76 (0.5)0.96 (1)7e40/15
P-DCN tran noiseless 1e70/15
P-zero tran noiseless 1e70/15
PRCGA sawyerr noiseless 19 (22)1e60/15
SMAC-BBOB hutter noiseless 10000/15
U-DCN tran noiseless 1e70/15
U-zero tran noiseless 1e70/15
fmincon pal noiseless 2e50/15
fminunc pal noiseless 25 (21)2e50/15
lmm-CMA-ES auger noiseless 0.70 (0.7)48050/15
simplex pal noiseless 2e50/15
tany liao noiseless 32 (25)43 (30)1e70/15
texp liao noiseless 1.9 (3)1.4 (2)1e70/15

Previous dimension | Dimension = 20 | Next dimension

Δ fopt
f1, 20-D
1e1
43
1e0
43
1e-1
43
1e-2
43
1e-3
43
1e-5
43
1e-7
43
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.2 (0.3)5.2 (0)7.3 (0)8.3 (0.5)10 (0)13 (0.5)16 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 3.7 (0.1)4.9 (0.8)6.2 (0.6)7.6 (0.5)8.9 (0.6)12 (0.5)15 (1.0)15/15
CGA-grid100 holtschulte noiseless 223 (46)574 (48)1496 (212)4236 (555)1.2e4 (4201)1e60/15
CGA-grid16 holtschulte noiseless 39 (9)105 (18)279 (72)704 (164)2128 (408)2.0e4 (2492)1e60/15
CGA-ring100 holtschulte noiseless 129 (26)333 (38)698 (79)1301 (136)2271 (209)8144 (1885)1e60/15
CGA-ring16 holtschulte noiseless 25 (4)67 (8)145 (22)329 (75)743 (112)6011 (971)1e60/15
CMAES Hutter hutter noiseless 7.8 (2)14 (2)20 (2)26 (1)33 (2)48 (1)20060/15
DE Pal pal noiseless 62 (9)140 (14)220 (15)298 (22)377 (14)530 (17)687 (15)15/15
GA-100 holtschulte noiseless 56 (10)152 (16)359 (26)723 (111)1518 (285)9101 (1501)1e60/15
HCMA loshchilov noiseless 1.00 (0.0)1.0 (0.0)1.0 (0.0)1.0 (0.0)1.0 (0.0)1.0 (0.0)1.0 (6e-3)15/15
HILL holtschulte noiseless 7.2 (2)21 (7)62 (13)188 (87)612 (131)5461 (1371)1e60/15
HMLSL pal noiseless 0.77 (0.2)1.7 (0.5)1.9 (0.2)2.2 (0.5)2.8 (0.2)3.7 (0.6)4.7 (0.5)15/15
IP-10DDr liao noiseless 7.5 (0.8)14 (0.7)20 (2)26 (0.4)32 (3)45 (1)57 (3)15/15
IP-500 liao noiseless 7.5 (1)14 (2)20 (2)26 (2)32 (3)45 (1)57 (3)15/15
IPOP400D auger noiseless 6.6 (0.5)13 (0.7)19 (1)25 (2)31 (2)44 (2)56 (3)15/15
IP liao noiseless 7.5 (0.3)14 (0.9)20 (1)26 (2)32 (2)45 (1)57 (3)15/15
MEMPSODE voglis noiseless 10 (7)16 (15)23 (23)25 (25)25 (25)25 (25)25 (25)15/15
MLSL pal noiseless 0.77 (0.2)1.7 (0.5)1.9 (0.2)2.2 (0.5)2.8 (0.2)3.7 (0.5)4.7 (0.4)15/15
OQNLP pal noiseless 1.2 (0)1.3 (0.3)1.7 (0.0)1.7 (0.0)1.8 (0.0)1.8 (0)1.8 (0)15/15
P-DCN tran noiseless 44 (14)63 (16)74 (18)89 (20)147 (32)702 (308)2421 (470)15/15
P-zero tran noiseless 45 (16)63 (16)71 (8)78 (13)100 (16)337 (84)2140 (549)15/15
PRCGA sawyerr noiseless 36 (7)72 (13)120 (29)182 (48)287 (67)1166 (458)6963 (6845)15/15
SMAC-BBOB hutter noiseless 0.97 (0.3)1.7 (0.2)3.3 (0.5)14 (4)112 (97)20000/15
U-DCN tran noiseless 21 (6)111 (39)378 (93)838 (274)1589 (520)4632 (1918)1.0e4 (2125)15/15
U-zero tran noiseless 8.6 (2)37 (6)119 (29)364 (166)1029 (269)1.0e4 (2803)1.1e5 (1e4)13/15
fmincon pal noiseless 0.77 (0.2)1.7 (0.5)1.9 (0.2)2.2 (0.5)2.8 (0.2)3.7 (0.5)4.7 (0.2)15/15
fminunc pal noiseless 1 (0)1 (0)1 (0)1 (0)1 (0)1 (0)1 (0)15/15
lmm-CMA-ES auger noiseless 5.6 (0.4)6.3 (0.1)6.8 (0.0)7.3 (0.1)7.8 (0.2)8.9 (0.2)10 (0.1)15/15
simplex pal noiseless 185 (126)6.4e4 (8e4)4e50/15
tany liao noiseless 7.7 (2)15 (1)22 (1)29 (1.0)36 (1)49 (3)61 (4)15/15
texp liao noiseless 6.6 (0.9)13 (1)20 (2)26 (0.9)33 (2)47 (2)59 (4)15/15

Δ fopt
f2, 20-D
1e1
385
1e0
386
1e-1
387
1e-2
388
1e-3
390
1e-5
391
1e-7
393
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (0.1)1.5 (0.1)1.7 (0.1)1.8 (0.1)2.1 (0.3)2.4 (0.2)2.8 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 4.3 (0.5)4.6 (0.7)4.9 (0.7)5.1 (0.8)5.4 (0.8)5.7 (0.8)6.1 (0.5)15/15
CGA-grid100 holtschulte noiseless 1763 (388)1e60/15
CGA-grid16 holtschulte noiseless 312 (225)1173 (632)3.8e4 (5e4)1e60/15
CGA-ring100 holtschulte noiseless 205 (27)510 (140)1620 (1765)1e60/15
CGA-ring16 holtschulte noiseless 173 (84)571 (349)2012 (1854)1.9e4 (2e4)1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 34 (2)43 (1)51 (2)60 (3)68 (2)85 (2)102 (2)15/15
GA-100 holtschulte noiseless 219 (106)643 (192)2434 (1290)1.9e4 (2e4)1e60/15
HCMA loshchilov noiseless 1.3 (0.1)1.5 (0.1)1.7 (0.0)1.8 (0.2)2.1 (0.3)2.4 (0.2)2.8 (0.2)15/15
HILL holtschulte noiseless 174 (143)487 (408)1993 (1737)1.9e4 (1e4)1e60/15
HMLSL pal noiseless 5.1 (2)5.7 (3)6.1 (3)6.4 (2)7.2 (3)10 (3)15 (17)15/15
IP-10DDr liao noiseless 35 (3)42 (4)48 (3)50 (3)51 (4)52 (1)53 (2)15/15
IP-500 liao noiseless 35 (2)42 (3)48 (5)50 (3)51 (2)52 (2)53 (2)15/15
IPOP400D auger noiseless 88110/15
IP liao noiseless 35 (4)42 (5)48 (4)50 (3)51 (2)52 (1)53 (2)15/15
MEMPSODE voglis noiseless 15 (10)18 (10)18 (16)19 (12)21 (6)25 (6)45 (34)15/15
MLSL pal noiseless 5.1 (3)5.7 (3)6.1 (3)6.4 (3)7.2 (3)10 (3)13 (4)15/15
OQNLP pal noiseless 4.2 (2)5.3 (2)6.5 (2)12 (3)12 (16)13 (1)3e50/15
P-DCN tran noiseless 25 (5)32 (5)52 (13)110 (42)257 (158)1017 (720)5820 (4094)13/15
P-zero tran noiseless 22 (3)28 (9)69 (76)221 (175)636 (143)4602 (2125)1.6e5 (1e5)2/15
PRCGA sawyerr noiseless 101 (432)200 (39)332 (847)698 (720)1401 (348)5407 (3070)1.7e4 (2e4)4/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 130 (47)374 (338)562 (234)679 (199)1534 (1073)2.1e4 (1e4)9.5e4 (9e4)3/15
U-zero tran noiseless 305 (104)1103 (429)4010 (2291)1.1e4 (9553)2.8e4 (9022)2e70/15
fmincon pal noiseless 5.6 (2)6.0 (2)6.4 (2)6.8 (2)7.4 (2)10 (3)14 (8)15/15
fminunc pal noiseless 19 (3)24 (10)36 (9)46 (21)68 (85)81 (46)106 (103)15/15
lmm-CMA-ES auger noiseless 8.4 (2)11 (1)12 (2)12 (0.8)13 (2)14 (2)15 (1)15/15
simplex pal noiseless 4e50/15
tany liao noiseless 35 (7)42 (4)46 (5)48 (3)50 (2)52 (2)53 (2)15/15
texp liao noiseless 34 (4)41 (5)45 (4)47 (3)49 (2)50 (1)51 (1)15/15

Δ fopt
f3, 20-D
1e1
5066
1e0
7626
1e-1
7635
1e-2
7637
1e-3
7643
1e-5
7646
1e-7
7651
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.26 (0.0)0.37 (0.1)0.46 (0.1)0.47 (0.1)0.49 (0.1)0.51 (0.0)0.53 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 20 (26)2e70/15
CGA-grid100 holtschulte noiseless 19 (3)54 (7)637 (860)1e60/15
CGA-grid16 holtschulte noiseless 3.4 (0.9)9.1 (2)31 (5)109 (16)1e60/15
CGA-ring100 holtschulte noiseless 7.2 (0.9)10 (0.6)18 (2)40 (11)131 (116)1e60/15
CGA-ring16 holtschulte noiseless 1.5 (0.2)3.4 (0.9)10 (2)33 (7)111 (34)1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 3.5 (0.4)6.2 (1)18 (3)46 (15)203 (70)1e60/15
HCMA loshchilov noiseless 0.26 (0.0)0.37 (0.1)0.46 (0.1)0.47 (0.1)0.49 (0.1)0.51 (0.1)0.53 (0.1)15/15
HILL holtschulte noiseless 0.83 (0.3)3.1 (2)10 (3)28 (8)87 (22)1e60/15
HMLSL pal noiseless 219 (207)4e50/15
IP-10DDr liao noiseless 15 (17)2e70/15
IP-500 liao noiseless 15 (12)1.9e4 (3e4)2e70/15
IPOP400D auger noiseless 88010/15
IP liao noiseless 15 (13)2e70/15
MEMPSODE voglis noiseless 16 (11)68 (16)110 (49)110 (48)110 (56)110 (52)116 (70)15/15
MLSL pal noiseless 4e50/15
OQNLP pal noiseless 3e50/15
P-DCN tran noiseless 145 (100)541 (606)753 (500)752 (221)752 (296)752 (696)751 (497)15/15
P-zero tran noiseless 216 (196)283 (87)378 (134)378 (171)378 (143)381 (113)508 (180)15/15
PRCGA sawyerr noiseless 3.1 (0.7)8.8 (4)11 (5)18 (11)19 (3)68 (102)275 (363)5/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 2.7 (0.6)9.5 (5)13 (5)21 (7)43 (24)138 (139)2113 (3978)5/15
U-zero tran noiseless 1.4 (0.2)4.8 (2)15 (7)55 (23)170 (77)1900 (444)2e70/15
fmincon pal noiseless 4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 88040/15
simplex pal noiseless 4e50/15
tany liao noiseless 10 (4)3.8e4 (7e4)2e70/15
texp liao noiseless 8.5 (2)3.9e4 (7e4)2e70/15

Δ fopt
f4, 20-D
1e1
4722
1e0
7628
1e-1
7666
1e-2
7686
1e-3
7700
1e-5
7758
1e-7
1.4e5
#succ
9/15
BIPOP-aCMA-STEP loshchilov noiseless 0.42 (0.0)0.67 (0.1)0.90 (0.1)1.1 (0.2)1.5 (0.2)1.8 (0.1)0.11 (9e-3)15/15
BIPOP-saACM-k loshchilov noiseless 1.9e4 (2e4)2e70/15
CGA-grid100 holtschulte noiseless 29 (4)74 (15)1e60/15
CGA-grid16 holtschulte noiseless 4.9 (0.9)13 (4)37 (8)216 (169)1e60/15
CGA-ring100 holtschulte noiseless 9.2 (0.5)12 (1)23 (4)52 (12)302 (259)1e60/15
CGA-ring16 holtschulte noiseless 2.3 (0.5)4.8 (2)16 (4)45 (10)373 (258)1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 620 (381)4e50/15
GA-100 holtschulte noiseless 4.7 (0.8)8.7 (4)23 (8)60 (14)641 (593)1e60/15
HCMA loshchilov noiseless 0.42 (0.1)0.67 (0.1)0.90 (0.1)1.1 (0.1)1.5 (0.2)1.8 (0.2)0.11 (0.0)15/15
HILL holtschulte noiseless 1.3 (0.2)3.6 (1)13 (6)44 (17)191 (118)1e60/15
HMLSL pal noiseless 622 (440)4e50/15
IP-10DDr liao noiseless 2.9e4 (3e4)2e70/15
IP-500 liao noiseless 2e70/15
IPOP400D auger noiseless 88010/15
IP liao noiseless 2e70/15
MEMPSODE voglis noiseless 22 (6)127 (108)183 (74)183 (73)182 (63)181 (92)10 (4)15/15
MLSL pal noiseless 4e50/15
OQNLP pal noiseless 3e50/15
P-DCN tran noiseless 214 (156)337 (292)447 (329)446 (292)445 (286)444 (297)25 (15)15/15
P-zero tran noiseless 270 (85)263 (72)375 (114)374 (203)373 (228)374 (237)28 (11)15/15
PRCGA sawyerr noiseless 5.6 (1)15 (4)20 (10)21 (15)29 (26)193 (149)50 (55)0/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 3.9 (0.6)12 (5)16 (7)28 (13)42 (14)219 (107)120 (121)5/15
U-zero tran noiseless 2.1 (0.6)6.9 (3)25 (10)78 (14)255 (74)3201 (1632)2e70/15
fmincon pal noiseless 4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 88130/15
simplex pal noiseless 4e50/15
tany liao noiseless 6.1e4 (7e4)2e70/15
texp liao noiseless 2e70/15

Δ fopt
f5, 20-D
1e1
41
1e0
41
1e-1
41
1e-2
41
1e-3
41
1e-5
41
1e-7
41
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.0 (0)1.0 (0)1.0 (0)1.0 (0)1.0 (0)1.0 (0)1.0 (0)15/15
BIPOP-saACM-k loshchilov noiseless 4.5 (1)5.2 (0.5)5.3 (0.8)5.3 (0.6)5.3 (0.7)5.3 (1)5.3 (1)15/15
CGA-grid100 holtschulte noiseless 343 (50)458 (77)477 (83)482 (82)482 (90)482 (61)482 (74)15/15
CGA-grid16 holtschulte noiseless 60 (9)74 (12)79 (11)80 (19)80 (16)80 (15)80 (16)15/15
CGA-ring100 holtschulte noiseless 185 (14)239 (19)261 (28)263 (22)263 (36)263 (30)263 (24)15/15
CGA-ring16 holtschulte noiseless 36 (5)47 (6)50 (3)51 (6)51 (5)51 (3)51 (6)15/15
CMAES Hutter hutter noiseless 5.6 (1)6.4 (1)6.6 (1)6.6 (1.0)6.6 (0.9)6.6 (1)6.6 (0.9)15/15
DE Pal pal noiseless 592 (62)1414 (109)2276 (101)3125 (171)3948 (156)5654 (268)7373 (309)15/15
GA-100 holtschulte noiseless 89 (11)117 (10)128 (11)132 (10)132 (14)132 (10)132 (17)15/15
HCMA loshchilov noiseless 1.2 (0.1)1.3 (0.3)1.4 (0.3)1.4 (0.1)1.4 (0.3)1.4 (0.4)1.4 (0.3)15/15
HILL holtschulte noiseless 11 (3)14 (5)15 (4)15 (4)15 (5)15 (4)15 (6)15/15
HMLSL pal noiseless 3.6 (0)5.1 (0)5.7 (0)6.2 (0)6.7 (0)7.2 (0)5359 (3873)14/15
IP-10DDr liao noiseless 50 (25)110 (54)163 (87)205 (106)231 (156)306 (271)400 (333)15/15
IP-500 liao noiseless 50 (104)110 (25)163 (75)205 (211)231 (188)306 (264)400 (173)15/15
IPOP400D auger noiseless 5.4 (1)6.3 (0.9)6.5 (1)6.5 (1)6.5 (1)6.5 (1)6.5 (1)15/15
IP liao noiseless 50 (103)110 (57)163 (144)205 (284)231 (221)306 (264)400 (262)15/15
MEMPSODE voglis noiseless 3.1 (0.2)3.1 (0.2)3.1 (0.2)3.1 (0.1)3.1 (0.2)3.1 (0.3)3.1 (0.2)15/15
MLSL pal noiseless 3.6 (0)5.1 (0)5.7 (0)6.2 (0)6.7 (0)7.2 (0)117 (81)1/15
OQNLP pal noiseless 1.3 (0)1.3 (0)1.3 (0)1.3 (0)1.3 (0)1.3 (0)1.3 (0)15/15
P-DCN tran noiseless 139 (39)188 (37)202 (76)217 (50)246 (29)333 (61)419 (22)15/15
P-zero tran noiseless 127 (20)162 (29)173 (30)178 (30)184 (32)198 (34)215 (22)15/15
PRCGA sawyerr noiseless 1.2e4 (2e4)1e60/15
SMAC-BBOB hutter noiseless 0.60 (0.1)★40.62 (0.2)★40.66 (0.1)★20.66 (0.2)★20.66 (0.1)★20.66 (0.4)★20.66 (0.1)★215/15
U-DCN tran noiseless 172 (64)933 (207)3014 (663)8376 (2853)1.6e4 (4058)1.3e6 (1e6)2e70/15
U-zero tran noiseless 91 (19)850 (302)1.1e4 (2263)1.3e5 (1e4)2e70/15
fmincon pal noiseless 3.6 (0)5.1 (0)5.7 (0)6.2 (0)6.7 (0)7.2 (0)102 (130)4/15
fminunc pal noiseless 2.1 (0)2.6 (0)2.6 (0)2.6 (0)2.6 (0)2.6 (0)2.6 (0)15/15
lmm-CMA-ES auger noiseless 5.0 (0.9)5.9 (1)6.1 (1)6.1 (0.6)6.1 (0.7)6.1 (0.8)6.1 (1)15/15
simplex pal noiseless 170 (44)225 (213)225 (207)225 (100)225 (96)225 (214)225 (86)15/15
tany liao noiseless 68 (143)133 (99)158 (173)183 (213)200 (281)233 (111)271 (326)15/15
texp liao noiseless 91 (124)175 (164)229 (195)277 (224)306 (253)354 (279)432 (239)15/15

Δ fopt
f6, 20-D
1e1
1296
1e0
2343
1e-1
3413
1e-2
4255
1e-3
5220
1e-5
6728
1e-7
8409
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.6 (0.3)1.3 (0.1)1.1 (0.1)1.1 (0.2)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1.6 (0.4)1.3 (0.4)1.2 (0.2)1.3 (0.2)1.4 (0.3)1.5 (0.2)1.7 (0.3)15/15
CGA-grid100 holtschulte noiseless 1211 (1081)1e60/15
CGA-grid16 holtschulte noiseless 443 (801)1260 (1423)4176 (4322)1e60/15
CGA-ring100 holtschulte noiseless 53 (9)99 (40)257 (208)3517 (3349)1e60/15
CGA-ring16 holtschulte noiseless 29 (60)367 (538)1278 (1249)3424 (5053)1e60/15
CMAES Hutter hutter noiseless 4.4 (5)20060/15
DE Pal pal noiseless 49 (7)63 (91)65 (63)72 (51)114 (79)4e50/15
GA-100 holtschulte noiseless 21 (4)78 (70)331 (582)3395 (4172)1e60/15
HCMA loshchilov noiseless 1.7 (0.3)1.4 (0.2)1.3 (0.2)1.3 (0.2)1.4 (0.2)1.6 (0.3)1.7 (0.4)15/15
HILL holtschulte noiseless 271 (394)1852 (1100)4258 (4322)1e60/15
HMLSL pal noiseless 1.8 (0.8)1.5 (0.8)1.5 (0.8)1.7 (0.9)1.8 (0.7)2.1 (0.7)2.5 (0.4)15/15
IP-10DDr liao noiseless 1.3 (0.2)1.1 (0.2)1.1 (0.2)1.1 (0.2)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
IP-500 liao noiseless 1.3 (0.2)1.1 (0.2)1.1 (0.2)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
IPOP400D auger noiseless 1.5 (0.3)1.2 (0.1)1.1 (0.1)1.1 (0.2)1.1 (0.2)1.2 (0.5)16 (14)0/15
IP liao noiseless 1.3 (0.2)1.1 (0.2)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
MEMPSODE voglis noiseless 7.6 (3)7.6 (2)7.8 (3)13 (7)19 (9)28 (12)63 (93)15/15
MLSL pal noiseless 1.8 (0.9)1.5 (0.9)1.5 (0.8)1.7 (1.0)1.8 (0.6)2.1 (0.2)2.7 (0.3)15/15
OQNLP pal noiseless 1.0 (0.7)1.4 (0.4)1.5 (1)8.8 (16)51 (33)3e50/15
P-DCN tran noiseless 16 (3)17 (2)470 (1517)1185 (874)2005 (1826)4356 (3046)1.1e4 (1e4)0/15
P-zero tran noiseless 9.2 (3)826 (3346)3139 (5650)8193 (1e4)1.6e4 (2e4)2e70/15
PRCGA sawyerr noiseless 461 (469)2045 (767)4301 (4999)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 358 (488)2573 (3420)3425 (3598)4165 (6339)6585 (5429)2e70/15
U-zero tran noiseless 3012 (4212)7234 (1e4)8.2e4 (7e4)6.6e4 (8e4)5.5e4 (6e4)2e70/15
fmincon pal noiseless 1.6 (0.3)1.4 (0.5)1.4 (0.6)1.6 (0.4)1.7 (0.9)2.0 (0.5)2.4 (0.4)15/15
fminunc pal noiseless 2.4 (1)2.7 (0.8)2.8 (0.4)2.9 (0.6)3.1 (0.5)6.1 (8)724 (715)0/15
lmm-CMA-ES auger noiseless 18 (16)56 (45)88040/15
simplex pal noiseless 4e50/15
tany liao noiseless 1.4 (0.2)1.2 (0.2)1.1 (0.2)1.1 (0.2)1.1 (0.2)1.2 (0.1)1.2 (0.1)15/15
texp liao noiseless 1.4 (0.3)1.2 (0.2)1.2 (0.2)1.2 (0.1)1.2 (0.2)1.3 (0.1)1.3 (0.2)15/15

Δ fopt
f7, 20-D
1e1
1351
1e0
4274
1e-1
9503
1e-2
16523
1e-3
16524
1e-5
16524
1e-7
16969
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.5 (1)3.2 (2)2.5 (1.0)1.5 (0.6)1.5 (0.6)1.5 (0.6)1.5 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 0.52 (0.2)1.2 (0.7)0.65 (0.3)0.55 (0.4)0.56 (0.2)0.56 (0.5)0.55 (0.5)15/15
CGA-grid100 holtschulte noiseless 5053 (4441)1e60/15
CGA-grid16 holtschulte noiseless 2371 (2906)1e60/15
CGA-ring100 holtschulte noiseless 93 (137)1e60/15
CGA-ring16 holtschulte noiseless 842 (1074)1e60/15
CMAES Hutter hutter noiseless 1.3 (2)20060/15
DE Pal pal noiseless 21 (7)77 (52)67 (67)118 (78)118 (61)118 (158)115 (112)2/15
GA-100 holtschulte noiseless 175 (306)1e60/15
HCMA loshchilov noiseless 0.98 (0.9)1.1 (0.5)0.84 (0.3)0.57 (0.5)0.57 (0.2)0.57 (0.5)0.57 (0.5)15/15
HILL holtschulte noiseless 2235 (1334)1e60/15
HMLSL pal noiseless 21 (4)72 (46)65 (29)116 (124)175 (173)175 (169)343 (153)1/15
IP-10DDr liao noiseless 1.7 (2)6.2 (2)3.9 (1)2.4 (0.9)2.4 (0.7)2.4 (1)2.4 (0.9)15/15
IP-500 liao noiseless 1.7 (3)6.2 (3)3.9 (2)2.4 (0.8)2.4 (1)2.4 (1)2.4 (1.0)15/15
IPOP400D auger noiseless 1.0 (0.7)29 (33)88270/15
IP liao noiseless 1.7 (3)6.2 (3)3.9 (2)2.4 (1.0)2.4 (1.0)2.4 (1)2.4 (1.0)15/15
MEMPSODE voglis noiseless 26 (25)340 (554)369 (147)247 (252)266 (96)266 (293)417 (544)11/15
MLSL pal noiseless 2e50/15
OQNLP pal noiseless 2e40/15
P-DCN tran noiseless 1.7e4 (2e4)2e70/15
P-zero tran noiseless 2528 (957)1.7e4 (2e4)2e70/15
PRCGA sawyerr noiseless 513 (662)1e60/15
SMAC-BBOB hutter noiseless 0.57 (0.3)20000/15
U-DCN tran noiseless 1.8e4 (2e4)2e70/15
U-zero tran noiseless 2.1e4 (2e4)2e70/15
fmincon pal noiseless 2e50/15
fminunc pal noiseless 2e50/15
lmm-CMA-ES auger noiseless 0.48 (0.1)88190/15
simplex pal noiseless 3e50/15
tany liao noiseless 1.0 (0.9)4.6 (1)3.2 (0.9)2.0 (0.4)2.0 (0.5)2.0 (0.4)1.9 (0.4)15/15
texp liao noiseless 1.6 (2)6.5 (5)3.7 (2)2.3 (1)2.3 (1)2.3 (2)2.2 (1.0)15/15

Δ fopt
f8, 20-D
1e1
2039
1e0
3871
1e-1
4040
1e-2
4148
1e-3
4219
1e-5
4371
1e-7
4484
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.7 (0.7)4.1 (3)4.4 (3)4.4 (3)4.5 (0.6)4.5 (2)4.5 (2)15/15
BIPOP-saACM-k loshchilov noiseless 1.0 (0.2)0.97 (0.1)1.0 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.1 (0.1)15/15
CGA-grid100 holtschulte noiseless 2244 (2656)1e60/15
CGA-grid16 holtschulte noiseless 611 (488)1112 (969)3657 (2042)1e60/15
CGA-ring100 holtschulte noiseless 3250 (5027)3670 (3487)3702 (4084)1e60/15
CGA-ring16 holtschulte noiseless 3367 (1638)3820 (2906)1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 13 (0.9)27 (26)27 (50)28 (24)29 (24)30 (0.7)32 (45)13/15
GA-100 holtschulte noiseless 1079 (1159)1829 (2002)1e60/15
HCMA loshchilov noiseless 1.3 (0.2)1.1 (0.1)1.2 (0.1)1.2 (0.1)1.2 (0.1)1.2 (0.1)1.2 (0.1)15/15
HILL holtschulte noiseless 260 (379)243 (262)1713 (1147)1e60/15
HMLSL pal noiseless 0.84 (0.2)1.0 (0.1)1.0 (1)1.0 (0.7)1.0 (0.8)1.0 (1)0.99 (0.7)15/15
IP-10DDr liao noiseless 4.1 (0.5)4.3 (0.5)4.6 (0.2)4.8 (0.4)4.8 (0.3)4.8 (0.4)4.9 (0.3)15/15
IP-500 liao noiseless 4.1 (0.7)4.3 (0.3)4.6 (0.3)4.8 (0.5)4.8 (0.4)4.8 (0.3)4.9 (0.3)15/15
IPOP400D auger noiseless 6.5 (5)88110/15
IP liao noiseless 4.1 (0.7)4.3 (0.2)4.6 (0.5)4.8 (0.3)4.8 (0.4)4.8 (0.3)4.9 (0.4)15/15
MEMPSODE voglis noiseless 6.4 (3)7.8 (4)8.2 (3)8.2 (6)8.6 (6)8.7 (6)8.5 (4)15/15
MLSL pal noiseless 0.84 (0.2)0.78 (0.6)0.79 (0.6)0.79 (0.4)0.79 (0.3)0.79 (0.5)0.78 (0.3)15/15
OQNLP pal noiseless 0.67 (0.1)0.68 (0.2)0.70 (0.4)0.71 (0.2)0.71 (0.1)0.70 (0.4)3e50/15
P-DCN tran noiseless 563 (238)1530 (1444)1717 (2636)2017 (2416)2408 (128)3376 (2506)1.3e4 (1e4)1/15
P-zero tran noiseless 215 (241)653 (56)959 (71)3021 (2451)2e70/15
PRCGA sawyerr noiseless 1116 (1161)1579 (1989)2138 (2942)6823 (1e4)6759 (8533)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 551 (576)767 (732)1198 (837)1824 (1017)2494 (1012)3.3e4 (3e4)2e70/15
U-zero tran noiseless 1382 (1193)2429 (2743)2.0e4 (1e4)2e70/15
fmincon pal noiseless 0.84 (0.2)0.84 (0.9)0.85 (0.8)0.85 (0.1)0.85 (0.1)0.84 (0.3)0.83 (0.4)15/15
fminunc pal noiseless 1.4 (0.3)1.1 (0.1)1.1 (0.1)1.1 (0.4)1.1 (0.4)1.0 (0.3)1.0 (0.3)15/15
lmm-CMA-ES auger noiseless 1.7 (0.3)2.1 (0.9)2.2 (0.1)2.2 (2)2.2 (3)2.2 (0.7)2.2 (2)12/15
simplex pal noiseless 4e50/15
tany liao noiseless 4.6 (1)5.1 (4)5.5 (4)5.6 (4)5.6 (0.4)5.6 (0.4)5.7 (2)15/15
texp liao noiseless 4.4 (0.6)5.0 (2)5.4 (4)5.5 (0.2)5.5 (0.1)5.5 (2)5.6 (0.3)15/15

Δ fopt
f9, 20-D
1e1
1716
1e0
3102
1e-1
3277
1e-2
3379
1e-3
3455
1e-5
3594
1e-7
3727
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.9 (0.8)4.1 (0.5)4.3 (0.3)4.4 (0.3)4.5 (0.5)4.5 (0.3)4.5 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 1.3 (0.3)1.3 (0.6)1.4 (0.2)1.4 (0.1)1.4 (0.5)1.4 (0.2)1.4 (0.1)15/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 1e60/15
CGA-ring100 holtschulte noiseless 1e60/15
CGA-ring16 holtschulte noiseless 1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 1e60/15
HCMA loshchilov noiseless 1.6 (0.2)1.5 (0.2)1.6 (1)1.6 (0.7)1.6 (0.2)1.6 (0.3)1.6 (0.5)15/15
HILL holtschulte noiseless 1e60/15
HMLSL pal noiseless 0.17 (0.0)0.34 (0.0)0.38 (0.0)0.39 (0.0)0.40 (0.0)0.40 (0.0)0.40 (0.0)15/15
IP-10DDr liao noiseless 5.0 (1)6.9 (4)7.2 (5)7.3 (0.3)7.3 (0.7)7.3 (4)7.2 (2)15/15
IP-500 liao noiseless 5.0 (2)6.9 (5)7.2 (2)7.3 (4)7.3 (4)7.3 (4)7.2 (4)15/15
IPOP400D auger noiseless 4.5 (0.6)88110/15
IP liao noiseless 5.0 (1)6.9 (4)7.2 (4)7.3 (0.4)7.3 (5)7.3 (4)7.2 (4)15/15
MEMPSODE voglis noiseless 8.8 (3)11 (5)15 (3)16 (5)17 (6)19 (4)20 (5)15/15
MLSL pal noiseless 0.17 (0.0)0.34 (0.0)0.38 (0.0)0.39 (0.0)0.40 (0.0)0.40 (0.0)0.40 (0.0)15/15
OQNLP pal noiseless 0.32 (2e-3)0.27 (6e-4)0.31 (9e-4)0.33 (1e-3)0.34 (5e-3)0.34 (2e-3)5.1 (13)4/15
P-DCN tran noiseless 1599 (782)5403 (3664)2e70/15
P-zero tran noiseless 412 (326)4135 (1657)6471 (3592)2e70/15
PRCGA sawyerr noiseless 688 (960)4337 (6392)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 1.7e4 (2e4)9.3e4 (1e5)2e70/15
U-zero tran noiseless 4.0e4 (3e4)2e70/15
fmincon pal noiseless 0.17 (0.0)0.34 (0.0)0.38 (0.0)0.39 (0.0)0.40 (0.0)0.40 (0.0)0.40 (0.0)15/15
fminunc pal noiseless 0.16 (0.0)0.26 (0.0)0.30 (0.0)0.32 (0.0)0.33 (8e-3)0.34 (0.0)0.33 (0.0)15/15
lmm-CMA-ES auger noiseless 2.1 (0.4)2.1 (0.2)2.2 (0.2)2.2 (0.2)2.4 (0.8)2.4 (0.7)2.7 (1)12/15
simplex pal noiseless 4e50/15
tany liao noiseless 5.0 (1)5.3 (0.2)5.7 (0.4)5.9 (0.7)6.0 (0.5)6.0 (0.3)6.0 (0.6)15/15
texp liao noiseless 4.8 (0.6)6.0 (6)6.3 (5)6.4 (5)6.5 (0.5)6.5 (3)6.5 (0.3)15/15

Δ fopt
f10, 20-D
1e1
7413
1e0
8661
1e-1
10735
1e-2
13641
1e-3
14920
1e-5
17073
1e-7
17476
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.2 (0.3)1.2 (0.2)1.0 (0.1)0.85 (0.1)0.80 (0.1)0.74 (0.1)0.76 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 0.21 (0.0)0.20 (0.0)0.17 (0.0)0.14 (0.0)0.13 (0.0)0.13 (0.0)0.13 (0.0)15/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 1e60/15
CGA-ring100 holtschulte noiseless 1e60/15
CGA-ring16 holtschulte noiseless 1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 1e60/15
HCMA loshchilov noiseless 0.25 (0.0)0.23 (0.0)0.20 (0.0)0.16 (0.0)0.15 (0.0)0.14 (0.0)0.15 (0.0)15/15
HILL holtschulte noiseless 1e60/15
HMLSL pal noiseless 0.13 (0.0)0.12 (0.0)0.11 (0.0)0.09 (0.0)0.12 (0.1)41 (67)4e50/15
IP-10DDr liao noiseless 1.8 (0.3)1.9 (0.2)1.7 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.0)1.2 (0.0)15/15
IP-500 liao noiseless 1.8 (0.3)1.9 (0.2)1.7 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.0)1.2 (0.0)15/15
IPOP400D auger noiseless 88110/15
IP liao noiseless 1.8 (0.2)1.9 (0.2)1.7 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.0)1.2 (0.0)15/15
MEMPSODE voglis noiseless 6.2 (4)6.8 (2)6.8 (9)6.0 (3)9.2 (7)59 (86)1e70/15
MLSL pal noiseless 0.13 (0.0)0.12 (0.0)0.11 (0.0)0.09 (0.0)0.12 (0.1)41 (117)4e50/15
OQNLP pal noiseless 0.54 (0.3)0.98 (0.9)3.6 (6)8.4 (16)61 (132)3e50/15
P-DCN tran noiseless 2e70/15
P-zero tran noiseless 2e70/15
PRCGA sawyerr noiseless 2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 2e70/15
U-zero tran noiseless 2e70/15
fmincon pal noiseless 0.15 (0.1)0.14 (0.1)0.12 (0.1)0.10 (0.1)0.10 (0.1)34 (36)4e50/15
fminunc pal noiseless 0.91 (0.2)1.1 (0.7)1.4 (0.8)1.7 (1)2.4 (1)10 (12)4e50/15
lmm-CMA-ES auger noiseless 0.46 (0.1)0.47 (0.1)0.41 (0.1)0.34 (0.0)0.33 (0.0)0.31 (0.0)0.32 (0.0)15/15
simplex pal noiseless 4e50/15
tany liao noiseless 1.8 (0.3)1.8 (0.2)1.6 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.1)1.2 (0.1)15/15
texp liao noiseless 1.7 (0.2)1.7 (0.2)1.6 (0.1)1.3 (0.1)1.2 (0.1)1.1 (0.0)1.1 (0.0)15/15

Δ fopt
f11, 20-D
1e1
1002
1e0
2228
1e-1
6278
1e-2
8586
1e-3
9762
1e-5
12285
1e-7
14831
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.8 (0.2)2.4 (0.2)0.91 (0.1)0.71 (0.0)0.66 (0.0)0.57 (0.0)0.52 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 1.6 (0.4)0.77 (0.2)0.29 (0.1)0.22 (0.0)0.20 (0.0)0.17 (0.1)0.15 (0.1)15/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 2753 (3749)1e60/15
CGA-ring100 holtschulte noiseless 808 (351)1e60/15
CGA-ring16 holtschulte noiseless 470 (211)1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 333 (203)1e60/15
HCMA loshchilov noiseless 1.7 (0.2)0.81 (0.1)0.30 (0.0)0.23 (0.0)0.21 (0.0)0.18 (0.0)0.16 (9e-3)15/15
HILL holtschulte noiseless 577 (244)1e60/15
HMLSL pal noiseless 0.17 (0.1)0.10 (0.0)0.04 (0.0)0.04 (8e-3)1.2 (3)4e50/15
IP-10DDr liao noiseless 10 (0.5)5.1 (0.2)2.0 (0.0)1.5 (0.1)1.4 (0.1)1.2 (0.0)1.1 (0.0)15/15
IP-500 liao noiseless 10 (0.5)5.1 (0.2)2.0 (0.1)1.5 (0.1)1.4 (0.0)1.2 (0.0)1.1 (0.0)15/15
IPOP400D auger noiseless 88110/15
IP liao noiseless 10 (0.5)5.1 (0.1)2.0 (0.0)1.5 (0.0)1.4 (0.0)1.2 (0.0)1.1 (0.0)15/15
MEMPSODE voglis noiseless 4.5 (0.7)2.2 (0.1)0.81 (0.1)0.64 (0.0)0.81 (0.6)20 (13)9880 (1e4)0/15
MLSL pal noiseless 0.17 (0.1)0.10 (0.0)0.04 (7e-3)0.04 (1e-2)0.86 (0.8)4e50/15
OQNLP pal noiseless 0.16 (0.0)0.18 (0.2)0.25 (0.1)0.62 (0.6)6.2 (8)1e50/15
P-DCN tran noiseless 457 (194)417 (95)211 (66)312 (175)850 (270)2e70/15
P-zero tran noiseless 676 (270)617 (218)349 (92)457 (85)1233 (778)2e70/15
PRCGA sawyerr noiseless 1.3e4 (8779)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 786 (772)3035 (1182)6177 (8144)2e70/15
U-zero tran noiseless 1213 (378)7557 (5458)2e70/15
fmincon pal noiseless 0.16 (0.1)0.10 (0.0)0.04 (0.0)0.04 (0.0)1.1 (0.1)228 (321)4e50/15
fminunc pal noiseless 0.51 (0.1)1.1 (0.4)0.97 (0.5)2.2 (2)81 (90)4e50/15
lmm-CMA-ES auger noiseless 2.1 (0.1)1.1 (0.3)0.43 (0.0)0.33 (0.0)0.31 (0.0)0.28 (0.0)0.25 (0.0)15/15
simplex pal noiseless 4e50/15
tany liao noiseless 9.4 (0.4)4.8 (0.2)1.9 (0.1)1.4 (0.1)1.3 (0.0)1.1 (0.0)0.99 (0.0)15/15
texp liao noiseless 8.4 (0.6)4.3 (0.2)1.7 (0.1)1.3 (0.1)1.2 (0.1)1.0 (0.0)0.90 (0.0)15/15

Δ fopt
f12, 20-D
1e1
1042
1e0
1938
1e-1
2740
1e-2
3156
1e-3
4140
1e-5
12407
1e-7
13827
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.1 (3)3.6 (3)3.8 (3)4.0 (2)3.5 (2)1.5 (0.6)1.5 (0.7)15/15
BIPOP-saACM-k loshchilov noiseless 0.83 (0.1)0.93 (1)1.2 (0.7)1.2 (0.6)1.1 (0.2)0.51 (0.1)0.53 (0.1)15/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 2611 (1495)1e60/15
CGA-ring100 holtschulte noiseless 605 (167)2563 (3731)1e60/15
CGA-ring16 holtschulte noiseless 571 (336)7558 (7740)1e60/15
CMAES Hutter hutter noiseless 4.8 (2)20060/15
DE Pal pal noiseless 102 (157)235 (222)1028 (1112)4e50/15
GA-100 holtschulte noiseless 720 (733)7711 (9675)1e60/15
HCMA loshchilov noiseless 1.7 (1)1.7 (1)1.6 (1)1.6 (0.7)1.4 (0.8)0.60 (0.1)0.61 (0.2)15/15
HILL holtschulte noiseless 685 (965)2450 (2291)1e60/15
HMLSL pal noiseless 0.81 (0.3)0.89 (0.6)0.83 (0.5)0.83 (0.5)0.72 (0.2)8.8 (9)37 (46)2/15
IP-10DDr liao noiseless 2.6 (3)3.6 (3)4.1 (3)4.5 (3)4.1 (2)1.8 (0.3)1.9 (0.6)15/15
IP-500 liao noiseless 2.6 (2)3.6 (3)4.1 (3)4.5 (2)4.1 (2)1.8 (0.6)1.9 (0.8)15/15
IPOP400D auger noiseless 2.3 (2)3.1 (2)8.0 (8)10 (8)32 (28)88110/15
IP liao noiseless 2.6 (2)3.6 (3)4.1 (3)4.5 (2)4.1 (2)1.8 (0.5)1.9 (0.5)15/15
MEMPSODE voglis noiseless 5.7 (4)4.6 (2)5.8 (2)6.5 (4)8.0 (5)6.6 (7)124 (295)8/15
MLSL pal noiseless 0.81 (0.7)0.89 (0.4)0.83 (0.4)0.83 (0.3)0.72 (0.3)0.58 (0.7)11 (5)3/15
OQNLP pal noiseless 1.1 (0.6)2.5 (0.3)5.9 (20)10 (22)24 (62)3e50/15
P-DCN tran noiseless 7015 (9610)4.1e4 (4e4)1.0e5 (1e5)8.9e4 (1e5)6.8e4 (3e4)2e70/15
P-zero tran noiseless 6995 (2e4)1.6e4 (2e4)4.7e4 (4e4)8.9e4 (1e5)2e70/15
PRCGA sawyerr noiseless 214 (141)1201 (803)2841 (3798)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 3163 (9643)1.2e4 (1e4)4.8e4 (7e4)2e70/15
U-zero tran noiseless 7487 (2e4)1.1e4 (9293)1.0e5 (1e5)2e70/15
fmincon pal noiseless 0.81 (0.5)0.91 (0.4)0.84 (0.3)0.84 (0.4)0.85 (0.6)0.75 (0.9)14 (26)4/15
fminunc pal noiseless 0.61 (0.2)0.75 (0.6)0.80 (0.4)0.85 (0.5)0.94 (0.2)4.4 (3)61 (67)0/15
lmm-CMA-ES auger noiseless 1.1 (0.1)1.1 (0.7)1.3 (1.0)1.4 (0.6)1.7 (1)0.92 (0.2)2.2 (2)4/15
simplex pal noiseless 4e50/15
tany liao noiseless 2.4 (1)2.7 (1)3.7 (2)4.0 (2)3.9 (1)1.7 (0.5)1.8 (0.4)15/15
texp liao noiseless 2.3 (0.1)3.0 (3)3.4 (3)4.0 (2)3.8 (1)1.7 (0.4)1.8 (0.4)15/15

Δ fopt
f13, 20-D
1e1
652
1e0
2021
1e-1
2751
1e-2
3507
1e-3
18749
1e-5
24455
1e-7
30201
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.0 (5)2.7 (2)4.4 (2)3.7 (2)0.89 (0.4)1.1 (0.5)1.1 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 1.1 (0.7)0.74 (0.4)0.85 (0.5)0.84 (0.2)0.17 (0.1)0.21 (0.1)0.22 (0.1)15/15
CGA-grid100 holtschulte noiseless 5138 (4357)1e60/15
CGA-grid16 holtschulte noiseless 1142 (2379)7248 (7669)1e60/15
CGA-ring100 holtschulte noiseless 275 (108)662 (279)1e60/15
CGA-ring16 holtschulte noiseless 960 (770)1613 (1363)1e60/15
CMAES Hutter hutter noiseless 2.9 (1.0)20060/15
DE Pal pal noiseless 50 (9)103 (203)2143 (2545)4e50/15
GA-100 holtschulte noiseless 518 (1146)1266 (1033)1e60/15
HCMA loshchilov noiseless 1.3 (0.3)0.90 (0.3)0.99 (0.9)1.1 (0.6)0.25 (0.2)0.27 (0.1)0.24 (0.1)15/15
HILL holtschulte noiseless 1220 (799)7253 (4701)1e60/15
HMLSL pal noiseless 1.1 (0.2)0.82 (1)13 (38)61 (57)43 (65)4e50/15
IP-10DDr liao noiseless 2.4 (0.2)4.3 (2)6.4 (4)7.8 (6)1.7 (1)2.2 (0.9)2.3 (1)15/15
IP-500 liao noiseless 2.4 (0.2)4.3 (4)6.4 (6)7.8 (4)1.7 (1)2.2 (1)2.3 (0.9)15/15
IPOP400D auger noiseless 4.2 (5)3.5 (4)6.6 (6)18 (19)88130/15
IP liao noiseless 2.4 (0.3)4.3 (5)6.4 (4)7.8 (4)1.7 (1)2.2 (0.8)2.3 (0.8)15/15
MEMPSODE voglis noiseless 8.2 (2)4.7 (2)4.2 (2)4.3 (0.1)2.2 (1)23 (19)367 (322)1/15
MLSL pal noiseless 1.1 (0.2)0.68 (0.8)0.97 (0.5)1.6 (1)0.59 (0.7)4e50/15
OQNLP pal noiseless 1.1 (0.0)0.50 (0.0)0.48 (0.0)6.8 (16)22 (24)2e50/15
P-DCN tran noiseless 1.5e4 (8e4)1.5e4 (4e4)1.0e5 (9e4)2e70/15
P-zero tran noiseless 2.7e4 (5e4)4.0e4 (2e4)4.7e4 (3e4)8.0e4 (7e4)1.6e4 (2e4)2e70/15
PRCGA sawyerr noiseless 847 (1531)2814 (5465)4951 (4886)2e60/15
SMAC-BBOB hutter noiseless 21 (15)20000/15
U-DCN tran noiseless 2.7e4 (2e4)4.0e4 (4e4)1.0e5 (2e5)2e70/15
U-zero tran noiseless 5050 (2e4)1.6e4 (1e4)1.0e5 (6e4)2e70/15
fmincon pal noiseless 1.1 (0.2)0.58 (0.1)0.79 (0.7)1.3 (0.9)0.55 (0.6)4e50/15
fminunc pal noiseless 1.4 (0.1)0.96 (0.1)0.97 (0.1)0.98 (0.1)20 (16)4e50/15
lmm-CMA-ES auger noiseless 2.0 (0.1)1.0 (0.1)0.99 (0.1)0.94 (0.1)0.22 (0.0)0.21 (0.0)0.21 (0.0)15/15
simplex pal noiseless 4e50/15
tany liao noiseless 4.3 (6)4.8 (2)6.7 (6)7.7 (6)1.7 (0.6)2.0 (1)2.5 (0.6)15/15
texp liao noiseless 3.8 (6)4.3 (4)6.9 (4)7.3 (5)1.7 (0.9)2.0 (0.8)2.2 (0.4)15/15

Δ fopt
f14, 20-D
1e1
75
1e0
239
1e-1
304
1e-2
451
1e-3
932
1e-5
1648
1e-7
15661
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.4 (2)3.3 (0.6)3.9 (0.7)4.2 (0.5)3.3 (0.4)3.9 (0.3)0.68 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 3.1 (1)1.8 (0.3)2.1 (0.5)2.1 (0.2)1.4 (0.1)1.3 (0.1)0.19 (0.0)15/15
CGA-grid100 holtschulte noiseless 100 (61)112 (21)258 (79)3.2e4 (5e4)1e60/15
CGA-grid16 holtschulte noiseless 22 (6)20 (6)43 (13)959 (1000)1e60/15
CGA-ring100 holtschulte noiseless 50 (8)62 (8)122 (16)526 (202)1e60/15
CGA-ring16 holtschulte noiseless 11 (3)12 (2)23 (4)250 (211)1e60/15
CMAES Hutter hutter noiseless 3.8 (2)2.8 (0.6)3.6 (0.4)3.9 (0.4)20060/15
DE Pal pal noiseless 22 (10)29 (2)42 (5)85 (15)4e50/15
GA-100 holtschulte noiseless 19 (10)24 (6)47 (10)528 (424)1e60/15
HCMA loshchilov noiseless 1.3 (0.4)2.7 (0.3)2.9 (0.9)2.8 (0.2)1.7 (0.1)1.5 (0.1)0.21 (0.0)15/15
HILL holtschulte noiseless 3.5 (0.8)3.6 (1)10 (2)322 (195)1e60/15
HMLSL pal noiseless 0.74 (0.2)0.49 (0.1)0.65 (0.1)0.88 (0.1)0.65 (0.1)0.67 (0.1)4e50/15
IP-10DDr liao noiseless 3.8 (0.7)2.7 (0.4)3.4 (0.3)4.2 (0.6)4.2 (0.6)6.3 (0.4)1.2 (0.1)15/15
IP-500 liao noiseless 3.8 (0.5)2.7 (0.5)3.4 (0.3)4.2 (0.3)4.2 (0.5)6.3 (0.4)1.2 (0.1)15/15
IPOP400D auger noiseless 2.5 (0.6)2.2 (0.3)3.1 (0.4)3.9 (0.4)3.9 (0.3)88110/15
IP liao noiseless 3.8 (0.6)2.7 (0.6)3.4 (0.3)4.2 (0.3)4.2 (0.3)6.3 (0.3)1.2 (0.1)15/15
MEMPSODE voglis noiseless 10 (1)11 (4)11 (6)10 (2)5.9 (1)4.3 (0.6)1e70/15
MLSL pal noiseless 0.74 (0.1)0.49 (0.0)0.65 (0.1)0.88 (0.1)0.65 (0.1)0.67 (0.1)4e50/15
OQNLP pal noiseless 1.1 (0.0)0.62 (0.1)0.71 (0.1)0.76 (0.1)0.52 (0.0)★37e40/15
P-DCN tran noiseless 22 (6)15 (2)14 (2)37 (22)1150 (286)2e70/15
P-zero tran noiseless 25 (9)15 (3)14 (3)21 (6)3204 (4996)2e70/15
PRCGA sawyerr noiseless 12 (7)16 (3)23 (5)126 (53)2132 (3128)2e60/15
SMAC-BBOB hutter noiseless 19 (16)20000/15
U-DCN tran noiseless 6.6 (2)15 (4)54 (17)470 (139)2815 (852)2e70/15
U-zero tran noiseless 4.0 (0.8)6.2 (1)22 (7)728 (429)2e70/15
fmincon pal noiseless 0.74 (0.3)0.49 (0.1)0.65 (0.1)0.88 (0.1)0.65 (0.1)0.68 (0.1)4e50/15
fminunc pal noiseless 1.0 (0.3)0.98 (0.3)1.2 (0.4)1.2 (0.3)0.86 (0.1)0.87 (0.1)4e50/15
lmm-CMA-ES auger noiseless 3.0 (0.6)2.2 (0.4)2.8 (0.3)3.0 (0.2)2.1 (0.1)2.2 (0.1)0.35 (0.0)15/15
simplex pal noiseless 37 (6)8121 (8070)4e50/15
tany liao noiseless 3.6 (0.4)3.0 (0.3)3.8 (0.3)4.6 (0.5)4.5 (0.4)6.4 (0.7)1.2 (0.1)15/15
texp liao noiseless 1.6 (0.5)2.3 (0.4)3.2 (0.3)4.1 (0.2)4.1 (0.4)5.8 (0.5)1.1 (0.1)15/15

Δ fopt
f15, 20-D
1e1
30378
1e0
1.5e5
1e-1
3.1e5
1e-2
3.2e5
1e-3
3.2e5
1e-5
4.5e5
1e-7
4.6e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.90 (0.8)1.5 (0.7)1.0 (0.5)1.0 (0.4)1.0 (0.5)0.76 (0.3)0.76 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 0.62 (0.8)1.8 (0.8)0.96 (0.3)0.96 (0.3)0.97 (0.3)0.71 (0.2)0.73 (0.2)15/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 1e60/15
CGA-ring100 holtschulte noiseless 1e60/15
CGA-ring16 holtschulte noiseless 1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 1e60/15
HCMA loshchilov noiseless 1.0 (0.5)1.5 (1)0.90 (0.6)0.90 (0.6)0.90 (0.2)0.66 (0.2)0.66 (0.4)15/15
HILL holtschulte noiseless 1e60/15
HMLSL pal noiseless 4e50/15
IP-10DDr liao noiseless 1.1 (0.6)0.99 (0.7)0.70 (0.2)0.71 (0.3)0.71 (0.3)0.53 (0.2)0.54 (0.2)15/15
IP-500 liao noiseless 1.1 (0.6)0.99 (0.4)0.71 (0.5)0.71 (0.3)0.72 (0.2)0.53 (0.1)0.54 (0.1)15/15
IPOP400D auger noiseless 88110/15
IP liao noiseless 1.1 (0.5)0.99 (0.7)0.70 (0.3)0.71 (0.2)0.71 (0.3)0.53 (0.2)0.54 (0.2)15/15
MEMPSODE voglis noiseless 38 (18)1e70/15
MLSL pal noiseless 4e50/15
OQNLP pal noiseless 3e50/15
P-DCN tran noiseless 2e70/15
P-zero tran noiseless 2e70/15
PRCGA sawyerr noiseless 925 (1235)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 2e70/15
U-zero tran noiseless 2e70/15
fmincon pal noiseless 4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 4.3 (8)88070/15
simplex pal noiseless 4e50/15
tany liao noiseless 0.88 (0.5)1.0 (0.3)0.77 (0.3)0.78 (0.3)0.78 (0.2)0.58 (0.1)0.59 (0.3)15/15
texp liao noiseless 0.69 (0.5)0.75 (0.4)0.52 (0.2)0.53 (0.2)0.54 (0.2)0.41 (0.1)0.42 (0.1)15/15

Δ fopt
f16, 20-D
1e1
1384
1e0
27265
1e-1
77015
1e-2
1.4e5
1e-3
1.9e5
1e-5
2.0e5
1e-7
2.2e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.3 (0.8)0.67 (0.5)1.0 (0.9)1.1 (1.0)1.1 (0.7)1.3 (0.2)1.2 (1)15/15
BIPOP-saACM-k loshchilov noiseless 1.3 (0.3)0.58 (0.3)0.46 (0.2)0.44 (0.3)0.41 (0.2)0.61 (0.4)1.0 (0.6)15/15
CGA-grid100 holtschulte noiseless 294 (230)1e60/15
CGA-grid16 holtschulte noiseless 276 (280)1e60/15
CGA-ring100 holtschulte noiseless 16 (4)1e60/15
CGA-ring16 holtschulte noiseless 106 (186)1e60/15
CMAES Hutter hutter noiseless 2.1 (3)20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 59 (2)1e60/15
HCMA loshchilov noiseless 1.8 (0.9)0.66 (0.4)0.52 (0.2)0.53 (0.4)0.49 (0.4)0.69 (0.4)1.1 (1)15/15
HILL holtschulte noiseless 322 (725)1e60/15
HMLSL pal noiseless 478 (466)4e50/15
IP-10DDr liao noiseless 1.2 (0.3)0.27 (0.3)0.42 (0.2)0.57 (0.4)0.78 (0.2)0.85 (0.8)0.79 (0.4)15/15
IP-500 liao noiseless 1.2 (0.4)0.27 (0.3)0.42 (0.2)0.57 (0.2)0.78 (0.2)0.83 (0.9)0.77 (0.7)15/15
IPOP400D auger noiseless 1.6 (0.7)88110/15
IP liao noiseless 1.2 (0.3)0.27 (0.3)0.42 (0.2)0.57 (0.4)0.78 (0.6)0.85 (0.2)0.79 (0.8)15/15
MEMPSODE voglis noiseless 8.5 (10)869 (1499)1e70/15
MLSL pal noiseless 1274 (801)4e50/15
OQNLP pal noiseless 642 (438)2e50/15
P-DCN tran noiseless 2687 (1e4)2e70/15
P-zero tran noiseless 2.3e4 (2e4)2e70/15
PRCGA sawyerr noiseless 4.8 (3)2e60/15
SMAC-BBOB hutter noiseless 0.76 (0.4)20000/15
U-DCN tran noiseless 2758 (3746)2e70/15
U-zero tran noiseless 7414 (9859)2e70/15
fmincon pal noiseless 675 (638)4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 1.2 (0.5)0.75 (1)88090/15
simplex pal noiseless 130 (103)4e50/15
tany liao noiseless 1.3 (0.4)0.29 (0.2)0.46 (0.3)0.49 (0.3)0.69 (0.3)0.73 (0.5)0.70 (0.4)15/15
texp liao noiseless 0.86 (0.3)0.16 (0.1)0.37 (0.2)0.38 (0.2)0.34 (0.0)0.47 (0.5)0.45 (0.5)15/15

Δ fopt
f17, 20-D
1e1
63
1e0
1030
1e-1
4005
1e-2
12242
1e-3
30677
1e-5
56288
1e-7
80472
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.2 (2)2.0 (4)1.00 (0.9)1.1 (1)0.94 (0.3)1.0 (0.5)1.1 (0.4)15/15
BIPOP-saACM-k loshchilov noiseless 2.8 (1)3.3 (13)3.8 (3)2.2 (1)1.5 (0.6)1.7 (1)1.6 (0.8)15/15
CGA-grid100 holtschulte noiseless 25 (29)1e60/15
CGA-grid16 holtschulte noiseless 21 (38)1e60/15
CGA-ring100 holtschulte noiseless 12 (8)1587 (1952)1e60/15
CGA-ring16 holtschulte noiseless 4.6 (3)1e60/15
CMAES Hutter hutter noiseless 1.8 (1)1.0 (0.5)0.91 (0.6)20060/15
DE Pal pal noiseless 8.2 (4)17 (2)14 (2)10 (3)10 (10)105 (85)4e50/15
GA-100 holtschulte noiseless 7.4 (2)8.9 (2)1e60/15
HCMA loshchilov noiseless 2.7 (4)2.8 (1)3.1 (3)2.1 (0.7)1.6 (0.7)1.8 (0.5)1.8 (0.5)15/15
HILL holtschulte noiseless 6895 (10000)1e60/15
HMLSL pal noiseless 24 (68)21 (7)18 (4)16 (3)15 (15)4e50/15
IP-10DDr liao noiseless 1.9 (0.3)0.78 (0.1)0.67 (0.8)1.1 (1)0.93 (0.6)1.1 (0.6)1.1 (0.0)15/15
IP-500 liao noiseless 1.9 (0.8)0.78 (0.2)0.67 (0.8)1.1 (1.0)0.93 (0.3)1.1 (0.8)1.1 (0.5)15/15
IPOP400D auger noiseless 0.79 (0.7)0.80 (0.2)0.80 (1)1.7 (1)88110/15
IP liao noiseless 1.9 (0.5)0.78 (0.1)0.67 (0.8)1.1 (1)0.93 (0.3)1.1 (0.3)1.1 (0.0)15/15
MEMPSODE voglis noiseless 39 (33)194 (114)2971 (5044)3341 (5517)1e70/15
MLSL pal noiseless 22 (48)4e50/15
OQNLP pal noiseless 100 (342)3e50/15
P-DCN tran noiseless 2.6 (1)2e70/15
P-zero tran noiseless 2.3e4 (8e4)2e70/15
PRCGA sawyerr noiseless 2.6 (3)490 (1457)1170 (1039)2e60/15
SMAC-BBOB hutter noiseless 0.92 (2)20000/15
U-DCN tran noiseless 1.9 (0.5)2e70/15
U-zero tran noiseless 1.7 (1)2e70/15
fmincon pal noiseless 21 (29)4e50/15
fminunc pal noiseless 19 (40)4e50/15
lmm-CMA-ES auger noiseless 1 (1)1.4 (0.4)0.80 (0.7)1.7 (2)4.1 (6)88050/15
simplex pal noiseless 25 (24)4e50/15
tany liao noiseless 1.7 (1.0)0.96 (0.2)0.75 (0.1)0.86 (0.6)0.64 (0.3)0.67 (0.2)0.68 (0.2)15/15
texp liao noiseless 1.2 (0.9)0.96 (0.2)0.99 (2)0.99 (0.5)0.82 (0.5)0.82 (0.3)0.73 (0.1)15/15

Δ fopt
f18, 20-D
1e1
621
1e0
3972
1e-1
19561
1e-2
28555
1e-3
67569
1e-5
1.3e5
1e-7
1.5e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.2 (0.2)1.0 (0.1)1.2 (2)1.4 (0.3)1.2 (0.5)1.2 (0.6)1.3 (0.6)15/15
BIPOP-saACM-k loshchilov noiseless 1.1 (1)3.2 (3)1.9 (0.7)2.3 (1)1.4 (0.8)1.4 (0.6)1.6 (0.6)15/15
CGA-grid100 holtschulte noiseless 1.1e4 (8857)1e60/15
CGA-grid16 holtschulte noiseless 2.4e4 (4e4)1e60/15
CGA-ring100 holtschulte noiseless 54 (32)1e60/15
CGA-ring16 holtschulte noiseless 814 (2015)1e60/15
CMAES Hutter hutter noiseless 0.93 (0.3)0.75 (0.5)20060/15
DE Pal pal noiseless 13 (4)19 (3)19 (17)4e50/15
GA-100 holtschulte noiseless 80 (1)1e60/15
HCMA loshchilov noiseless 1.4 (0.2)2.7 (2)1.3 (0.4)1.6 (0.9)1.1 (0.7)1.1 (0.6)1.2 (0.4)15/15
HILL holtschulte noiseless 1e60/15
HMLSL pal noiseless 18 (2)22 (5)20 (4)4e50/15
IP-10DDr liao noiseless 0.87 (0.2)0.46 (0.1)0.66 (0.4)1.4 (0.7)1.2 (0.7)0.96 (0.2)1.0 (0.4)15/15
IP-500 liao noiseless 0.87 (0.1)0.46 (0.2)0.66 (0.4)1.4 (0.5)1.2 (0.9)0.96 (0.4)1.0 (0.3)15/15
IPOP400D auger noiseless 0.74 (0.3)0.67 (0.1)3.1 (4)88110/15
IP liao noiseless 0.87 (0.2)0.46 (0.1)0.66 (0.4)1.4 (0.9)1.2 (0.9)0.96 (0.4)1.0 (0.4)15/15
MEMPSODE voglis noiseless 81 (55)659 (973)2243 (2793)4974 (3504)1e70/15
MLSL pal noiseless 4e50/15
OQNLP pal noiseless 1713 (2016)3e50/15
P-DCN tran noiseless 2e70/15
P-zero tran noiseless 2e70/15
PRCGA sawyerr noiseless 3.9 (1)515 (388)2e60/15
SMAC-BBOB hutter noiseless 22 (13)20000/15
U-DCN tran noiseless 1.7e4 (4e4)2e70/15
U-zero tran noiseless 7.5e4 (5e4)2e70/15
fmincon pal noiseless 4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 0.76 (0.3)1.5 (2)6.4 (6)88040/15
simplex pal noiseless 4e50/15
tany liao noiseless 0.85 (0.2)0.45 (0.1)0.48 (0.6)1.2 (0.8)0.92 (0.4)0.87 (0.5)0.86 (0.5)15/15
texp liao noiseless 0.97 (0.3)1.3 (0.8)0.85 (0.6)1.3 (0.6)0.84 (0.3)0.80 (0.4)0.80 (0.3)15/15

Δ fopt
f19, 20-D
1e1
1
1e0
1
1e-1
3.4e5
1e-2
4.7e6
1e-3
6.2e6
1e-5
6.7e6
1e-7
6.7e6
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 259 (79)2.7e4 (2e4)1.2 (2)0.94 (0.6)0.86 (0.3)0.94 (0.2)0.94 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 148 (46)3.3e4 (3e4)0.72 (0.3)0.82 (0.3)0.76 (0.2)0.77 (0.2)0.77 (0.3)15/15
CGA-grid100 holtschulte noiseless 4258 (2126)1e60/15
CGA-grid16 holtschulte noiseless 1200 (330)1e60/15
CGA-ring100 holtschulte noiseless 2654 (608)1e60/15
CGA-ring16 holtschulte noiseless 596 (99)1e60/15
CMAES Hutter hutter noiseless 180 (58)20060/15
DE Pal pal noiseless 1337 (456)4e50/15
GA-100 holtschulte noiseless 1023 (286)1e60/15
HCMA loshchilov noiseless 49 (28)3.5e4 (2e4)0.72 (0.4)1.0 (0.6)0.95 (0.3)0.96 (0.3)0.96 (0.3)15/15
HILL holtschulte noiseless 1100 (2053)1e60/15
HMLSL pal noiseless 1 (0)1 (0)7.3e-4 (0)4e50/15
IP-10DDr liao noiseless 178 (148)5.2e5 (5858)4.0 (8)0.97 (0.3)0.84 (0.4)1.0 (0.7)1.0 (0.9)15/15
IP-500 liao noiseless 178 (148)5.2e5 (2e6)4.0 (0.9)11 (12)2e70/15
IPOP400D auger noiseless 1 (0)1 (0)88110/15
IP liao noiseless 178 (148)5.2e5 (2e6)4.0 (12)0.84 (0.7)0.67 (0.5)0.66 (0.2)0.66 (0.2)15/15
MEMPSODE voglis noiseless 4084 (4879)1.8e5 (9e4)134 (95)1e70/15
MLSL pal noiseless 1 (0)1 (0)7.3e-4 (0)4e50/15
OQNLP pal noiseless 1 (0)1 (0)5.4e-4 (1e-6)★41e50/15
P-DCN tran noiseless 4.3e6 (1e7)2e70/15
P-zero tran noiseless 3.2e7 (7e7)2e70/15
PRCGA sawyerr noiseless 199 (16)931 (519)0.35 (0.2)2e60/15
SMAC-BBOB hutter noiseless 1 (0)1 (0)20000/15
U-DCN tran noiseless 397 (322)2.9e8 (6e8)2e70/15
U-zero tran noiseless 317 (201)2e70/15
fmincon pal noiseless 1 (0)1 (0)7.3e-4 (1e-6)4e50/15
fminunc pal noiseless 1 (0)1 (0)6.5e-4 (5e-5)4e50/15
lmm-CMA-ES auger noiseless 1 (0)1 (0)88050/15
simplex pal noiseless 1 (0)1 (0)0.18 (0.6)4e50/15
tany liao noiseless 130 (116)3.6e4 (7e4)3.7 (4)0.79 (0.2)0.69 (0.1)0.70 (0.3)0.70 (0.5)15/15
texp liao noiseless 3.3 (2)4.5e4 (7e4)2.0 (1)0.63 (0.5)0.67 (0.6)0.80 (0.8)0.80 (0.6)15/15

Δ fopt
f20, 20-D
1e1
82
1e0
46150
1e-1
3.1e6
1e-2
5.5e6
1e-3
5.5e6
1e-5
5.6e6
1e-7
5.6e6
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 6.3 (0.4)4.7 (2)1.0 (0.6)0.95 (0.3)0.95 (0.2)0.95 (0.3)0.95 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 2.8 (0.7)2.4 (2)1.1 (0.4)0.93 (0.3)0.93 (0.3)0.93 (0.3)0.94 (0.3)15/15
CGA-grid100 holtschulte noiseless 153 (32)3.2 (2)1e60/15
CGA-grid16 holtschulte noiseless 27 (5)0.50 (0.2)1e60/15
CGA-ring100 holtschulte noiseless 74 (7)0.65 (0.1)0.68 (0.5)0.53 (0.7)0.54 (0.5)1.3 (1)1e60/15
CGA-ring16 holtschulte noiseless 17 (3)0.17 (0.1)1e60/15
CMAES Hutter hutter noiseless 4.7 (2)20060/15
DE Pal pal noiseless 36 (5)2.8 (1)4e50/15
GA-100 holtschulte noiseless 35 (6)0.39 (0.1)1e60/15
HCMA loshchilov noiseless 0.77 (0.2)1.9 (1.0)1.2 (0.7)0.88 (0.3)0.88 (0.3)0.88 (0.3)0.88 (0.3)15/15
HILL holtschulte noiseless 5.6 (2)0.13 (0.1)4.6 (2)1e60/15
HMLSL pal noiseless 1.4 (0)1.6 (0.4)1.9 (2)4e50/15
IP-10DDr liao noiseless 5.4 (1)5.6 (3)0.91 (0.5)1.5 (0.7)1.5 (1.0)1.5 (1)1.5 (1)15/15
IP-500 liao noiseless 5.4 (1.0)5.8 (2)2e70/15
IPOP400D auger noiseless 3.8 (0.6)88010/15
IP liao noiseless 5.4 (1)5.6 (2)0.86 (0.4)0.66 (0.1)0.66 (0.1)0.66 (0.1)0.67 (0.0)15/15
MEMPSODE voglis noiseless 26 (15)1.1 (1.0)6.7 (7)27 (20)27 (19)27 (29)27 (24)1/15
MLSL pal noiseless 1.4 (0)11 (8)4e50/15
OQNLP pal noiseless 0.89 (0)23 (31)2e50/15
P-DCN tran noiseless 22 (4)11 (11)2e70/15
P-zero tran noiseless 22 (6)77 (57)2e70/15
PRCGA sawyerr noiseless 11 (4)10 (12)2e60/15
SMAC-BBOB hutter noiseless 1.0 (0.1)20000/15
U-DCN tran noiseless 16 (10)1.4 (0.3)93 (95)52 (37)52 (49)51 (51)51 (47)1/15
U-zero tran noiseless 9.4 (6)0.32 (0.6)2e70/15
fmincon pal noiseless 1.4 (0)10 (7)4e50/15
fminunc pal noiseless 0.78 (0)2.0 (1)4e50/15
lmm-CMA-ES auger noiseless 3.6 (0.8)88200/15
simplex pal noiseless 88 (58)4e50/15
tany liao noiseless 5.5 (1)8.3 (4)0.81 (0.4)1.3 (2)1.3 (1)1.3 (1.0)1.3 (2)14/15
texp liao noiseless 2.6 (0.9)13 (0.4)48 (97)2e70/15

Δ fopt
f21, 20-D
1e1
561
1e0
6541
1e-1
14103
1e-2
14318
1e-3
14643
1e-5
15567
1e-7
17589
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.8 (8)80 (203)53 (40)52 (76)51 (81)48 (38)43 (24)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (7)3.7 (5)20 (4)20 (2)19 (4)19 (63)17 (57)15/15
CGA-grid100 holtschulte noiseless 1276 (4109)1e60/15
CGA-grid16 holtschulte noiseless 655 (3)612 (841)284 (301)281 (559)277 (359)271 (338)263 (319)0/15
CGA-ring100 holtschulte noiseless 14 (4)30 (44)29 (90)31 (36)34 (35)42 (36)54 (70)8/15
CGA-ring16 holtschulte noiseless 279 (891)230 (229)284 (301)280 (350)275 (427)262 (257)239 (186)3/15
CMAES Hutter hutter noiseless 2.5 (4)2.1 (3)0.98 (0.6)0.98 (1)0.97 (1)0.94 (1)0.85 (2)1/15
DE Pal pal noiseless 62 (179)94 (138)58 (121)57 (35)56 (89)54 (90)48 (57)5/15
GA-100 holtschulte noiseless 7.1 (2)612 (612)285 (266)281 (157)276 (324)265 (194)248 (467)3/15
HCMA loshchilov noiseless 0.76 (2)3.5 (0.8)49 (26)48 (25)47 (147)44 (160)39 (142)15/15
HILL holtschulte noiseless 2038 (2228)1e60/15
HMLSL pal noiseless 4.2 (9)11 (1)11 (36)11 (28)11 (7)10 (13)9.3 (7)7/15
IP-10DDr liao noiseless 6.3 (16)147 (412)430 (342)424 (60)414 (916)390 (81)345 (561)14/15
IP-500 liao noiseless 6.3 (16)856 (1223)2850 (3191)2807 (2459)2745 (1707)2582 (3534)2285 (3980)5/15
IPOP400D auger noiseless 5.8 (6)5.7 (10)4.3 (7)4.2 (4)4.2 (8)4.0 (4)3.5 (4)2/15
IP liao noiseless 6.3 (6)924 (776)2859 (5318)2817 (3868)2755 (4097)2592 (5139)2295 (2890)5/15
MEMPSODE voglis noiseless 4.9 (7)20 (28)22 (29)21 (18)21 (31)20 (13)19 (27)15/15
MLSL pal noiseless 1.3 (2)1.0 (2)1.00 (0.2)0.99 (2)0.98 (1)0.94 (1)0.91 (1)8/15
OQNLP pal noiseless 0.55 (0.7)1.8 (0.4)2.0 (4)1.9 (2)1.9 (1)2.0 (3)5e40/15
P-DCN tran noiseless 2.4e4 (4e4)4.3e4 (3e4)2.0e4 (2e4)2.0e4 (4e4)1.9e4 (2e4)1.8e4 (2e4)1.6e4 (1e4)1/15
P-zero tran noiseless 5488 (3e4)2.0e4 (2e4)9218 (1e4)9080 (2e4)8878 (1e4)8351 (1e4)7392 (9097)2/15
PRCGA sawyerr noiseless 1215 (10)3802 (4617)2e60/15
SMAC-BBOB hutter noiseless 3.5 (4)4.3 (8)20000/15
U-DCN tran noiseless 8916 (3)2.0e4 (2e4)9219 (1e4)9081 (6636)8882 (8195)8362 (7709)7414 (5401)2/15
U-zero tran noiseless 1.8e4 (4e4)2.0e4 (5e4)9218 (1e4)9080 (1e4)8880 (2e4)8356 (1e4)7407 (6822)2/15
fmincon pal noiseless 1.00 (2)0.62 (1)0.46 (0.6)0.46 (0.6)0.46 (0.6)0.46 (0.5)0.48 (0.6)9/15
fminunc pal noiseless 1.3 (2)0.82 (1)1.0 (2)1.0 (4)1.0 (4)1.0 (0.5)10 (15)4/15
lmm-CMA-ES auger noiseless 1.7 (2)1.8 (4)1.4 (1)1.4 (0.8)1.4 (2)1.3 (1)1.2 (1.0)5/15
simplex pal noiseless 11 (9)90 (53)4e50/15
tany liao noiseless 2.5 (2)51 (82)479 (583)471 (754)461 (755)434 (847)384 (593)12/15
texp liao noiseless 2.9 (7)47 (50)70 (69)69 (97)67 (93)64 (78)56 (68)15/15

Δ fopt
f22, 20-D
1e1
467
1e0
5580
1e-1
23491
1e-2
24163
1e-3
24948
1e-5
26847
1e-7
1.3e5
#succ
12/15
BIPOP-aCMA-STEP loshchilov noiseless 63 (68)220 (391)288 (486)280 (362)272 (335)252 (329)50 (70)14/15
BIPOP-saACM-k loshchilov noiseless 7.6 (2)221 (411)311 (289)303 (501)293 (430)273 (412)54 (74)13/15
CGA-grid100 holtschulte noiseless 3245 (2149)1170 (1076)1e60/15
CGA-grid16 holtschulte noiseless 2456 (2141)1171 (941)622 (543)1e60/15
CGA-ring100 holtschulte noiseless 17 (8)125 (225)1e60/15
CGA-ring16 holtschulte noiseless 333 (2143)494 (1120)1e60/15
CMAES Hutter hutter noiseless 3.1 (2)2.5 (2)20060/15
DE Pal pal noiseless 584 (434)200 (431)4e50/15
GA-100 holtschulte noiseless 787 (1071)1166 (1120)1e60/15
HCMA loshchilov noiseless 11 (18)135 (431)486 (364)473 (554)458 (605)425 (760)85 (77)11/15
HILL holtschulte noiseless 780 (1606)1165 (762)1e60/15
HMLSL pal noiseless 140 (226)64 (126)111 (175)108 (199)105 (72)97 (101)42 (79)1/15
IP-10DDr liao noiseless 96 (87)1871 (1942)2e70/15
IP-500 liao noiseless 525 (247)2405 (3589)2e70/15
IPOP400D auger noiseless 11 (24)10 (9)88010/15
IP liao noiseless 96 (168)2411 (4488)2e70/15
MEMPSODE voglis noiseless 29 (150)47 (28)279 (467)272 (430)263 (375)245 (172)75 (126)4/15
MLSL pal noiseless 3.2 (5)3.4 (2)4.3 (5)4.2 (4)4.1 (4)3.8 (6)0.82 (1)5/15
OQNLP pal noiseless 3.1 (4)5.4 (6)8.3 (12)8.1 (13)8.2 (9)27 (17)5e40/15
P-DCN tran noiseless 3.7e4 (5e4)2.3e4 (2e4)2e70/15
P-zero tran noiseless 2.9e4 (7e4)2.3e4 (1e4)2e70/15
PRCGA sawyerr noiseless 867 (1964)1121 (1962)2e60/15
SMAC-BBOB hutter noiseless 3.3 (8)20000/15
U-DCN tran noiseless 2.9e4 (2)2e70/15
U-zero tran noiseless 2.1e4 (3e4)2e70/15
fmincon pal noiseless 4.2 (3)3.1 (2)4.8 (4)4.7 (5)4.5 (6)4.3 (6)1.3 (2)5/15
fminunc pal noiseless 2.4 (2)3.2 (5)7.0 (8)6.8 (8)6.6 (8)6.2 (7)9.4 (8)1/15
lmm-CMA-ES auger noiseless 6.7 (10)4.7 (4)88110/15
simplex pal noiseless 64 (20)1073 (2100)4e50/15
tany liao noiseless 83 (5)1944 (4541)2e70/15
texp liao noiseless 62 (42)532 (2190)502 (483)488 (554)473 (517)440 (704)88 (103)12/15

Δ fopt
f23, 20-D
1e1
3.0
1e0
1614
1e-1
67457
1e-2
3.7e5
1e-3
4.9e5
1e-5
8.1e5
1e-7
8.4e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 2.4 (3)23 (22)0.69 (0.7)1.5 (2)2.3 (3)1.4 (0.7)1.5 (2)15/15
BIPOP-saACM-k loshchilov noiseless 3.4 (3)29 (14)0.74 (0.5)0.83 (0.2)2.7 (3)1.8 (2)1.9 (3)15/15
CGA-grid100 holtschulte noiseless 2.3 (2)2274 (3686)1e60/15
CGA-grid16 holtschulte noiseless 2.7 (2)459 (567)1e60/15
CGA-ring100 holtschulte noiseless 2.2 (3)274 (85)1e60/15
CGA-ring16 holtschulte noiseless 1.5 (2)264 (367)1e60/15
CMAES Hutter hutter noiseless 3.8 (3)20060/15
DE Pal pal noiseless 2.0 (2)4e50/15
GA-100 holtschulte noiseless 1.7 (1)1486 (2684)1e60/15
HCMA loshchilov noiseless 13 (10)23 (14)0.96 (0.6)1.0 (0.7)1.8 (2)1.1 (1)1.1 (1.0)15/15
HILL holtschulte noiseless 2.3 (1)1120 (1007)1e60/15
HMLSL pal noiseless 12 (20)6.4 (5)86 (81)4e50/15
IP-10DDr liao noiseless 1.8 (1)35 (23)5.3 (4)30 (41)71 (87)43 (77)41 (59)7/15
IP-500 liao noiseless 1.8 (2)35 (30)5.3 (4)29 (30)72 (82)44 (50)42 (49)7/15
IPOP400D auger noiseless 2.7 (4)81 (97)88010/15
IP liao noiseless 1.8 (2)35 (54)5.3 (4)40 (57)100 (107)60 (93)58 (85)5/15
MEMPSODE voglis noiseless 3.3 (4)25 (14)75 (37)1e70/15
MLSL pal noiseless 12 (25)3.4 (2)25 (21)4e50/15
OQNLP pal noiseless 57 (132)3.5 (3)2e50/15
P-DCN tran noiseless 2.2 (2)1083 (6309)2e70/15
P-zero tran noiseless 2.3 (2)2304 (1059)2e70/15
PRCGA sawyerr noiseless 2.1 (2)2615 (2042)1e60/15
SMAC-BBOB hutter noiseless 1.8 (2)20000/15
U-DCN tran noiseless 2.3 (2)4711 (5691)2e70/15
U-zero tran noiseless 2.6 (3)3936 (6489)2e70/15
fmincon pal noiseless 11 (14)4.4 (8)90 (113)4e50/15
fminunc pal noiseless 19 (26)248 (235)4e50/15
lmm-CMA-ES auger noiseless 1.8 (1)88230/15
simplex pal noiseless 187 (236)1.9 (0.2)4e50/15
tany liao noiseless 1.8 (1)20 (23)3.0 (6)53 (69)55 (55)51 (45)49 (38)6/15
texp liao noiseless 1.4 (1)28 (48)28 (134)93 (63)182 (199)110 (99)106 (131)3/15

Δ fopt
f24, 20-D
1e1
1.3e6
1e0
7.5e6
1e-1
5.2e7
1e-2
5.2e7
1e-3
5.2e7
1e-5
5.2e7
1e-7
5.2e7
#succ
3/15
BIPOP-aCMA-STEP loshchilov noiseless 1.7 (2)0.90 (1)2.7 (3)2.7 (2)2.7 (2)2.7 (3)2.7 (5)2/15
BIPOP-saACM-k loshchilov noiseless 1.3 (4)0.93 (0.9)1.2 (2)1.2 (2)1.2 (1)1.2 (2)1.2 (1)4/15
CGA-grid100 holtschulte noiseless 1e60/15
CGA-grid16 holtschulte noiseless 1e60/15
CGA-ring100 holtschulte noiseless 1e60/15
CGA-ring16 holtschulte noiseless 1e60/15
CMAES Hutter hutter noiseless 20060/15
DE Pal pal noiseless 4e50/15
GA-100 holtschulte noiseless 1e60/15
HCMA loshchilov noiseless 0.88 (1)1.2 (1.0)5.7 (4)5.7 (6)5.7 (4)5.7 (8)5.7 (9)1/15
HILL holtschulte noiseless 1e60/15
HMLSL pal noiseless 4e50/15
IP-10DDr liao noiseless 2e70/15
IP-500 liao noiseless 2e70/15
IPOP400D auger noiseless 88110/15
IP liao noiseless 2e70/15
MEMPSODE voglis noiseless 31 (58)1e70/15
MLSL pal noiseless 4e50/15
OQNLP pal noiseless 3e50/15
P-DCN tran noiseless 2e70/15
P-zero tran noiseless 2e70/15
PRCGA sawyerr noiseless 21 (20)2e60/15
SMAC-BBOB hutter noiseless 20000/15
U-DCN tran noiseless 2e70/15
U-zero tran noiseless 2e70/15
fmincon pal noiseless 4e50/15
fminunc pal noiseless 4e50/15
lmm-CMA-ES auger noiseless 88170/15
simplex pal noiseless 4e50/15
tany liao noiseless 28 (35)2e70/15
texp liao noiseless 1.2 (2)0.68 (0.6)5.5 (2)5.5 (4)5.5 (5)5.5 (8)5.5 (8)1/15

Previous dimension | Dimension = 40 | First dimension

Δ fopt
f1, 40-D
1e1
83
1e0
83
1e-1
83
1e-2
83
1e-3
83
1e-5
83
1e-7
83
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 4.5 (0)6.3 (0)7.4 (0)9.3 (0)11 (0.2)14 (0)17 (0)15/15
BIPOP-saACM-k loshchilov noiseless 3.1 (0.5)4.5 (0.5)5.4 (0.2)6.5 (0.4)7.8 (0.7)10 (0.6)12 (0.8)15/15
CGA-grid100 holtschulte noiseless 374 (52)923 (101)2326 (308)6547 (1462)1.9e4 (2134)2e60/15
CGA-grid16 holtschulte noiseless 60 (7)152 (10)412 (55)1146 (184)3334 (409)2e60/15
CGA-ring100 holtschulte noiseless 195 (11)456 (33)893 (47)1582 (112)2625 (183)1.1e4 (953)2e60/15
CGA-ring16 holtschulte noiseless 36 (2)84 (3)188 (17)414 (46)1071 (234)9329 (1266)2e60/15
CMAES Hutter hutter noiseless 10 (0.6)16 (1)22 (1)28 (0.9)34 (1)46 (0.8)40070/15
GA-100 holtschulte noiseless 78 (9)206 (26)462 (25)990 (72)2192 (360)1.4e4 (3807)2e60/15
HILL holtschulte noiseless 11 (2)29 (7)95 (23)290 (53)892 (225)9553 (3006)2e60/15
IP-10DDr liao noiseless 9.1 (0.5)15 (0.5)21 (0.8)27 (1.0)33 (1)45 (0.7)57 (1)15/15
IP-500 liao noiseless 9.1 (0.5)15 (0.8)21 (0.9)27 (0.9)33 (0.9)45 (1)57 (1)15/15
IP liao noiseless 9.1 (0.4)15 (0.5)21 (1)27 (1)33 (1.0)45 (2)57 (1)15/15
MEMPSODE voglis noiseless 1.7 (0)★41.7 (0)★41.7 (0)★41.7 (0)★41.7 (0)★41.7 (0)★41.7 (0)★415/15
PRCGA sawyerr noiseless 46 (8)94 (10)160 (12)265 (38)469 (183)1529 (541)3922 (1997)15/15
tany liao noiseless 9.0 (0.5)15 (0.8)22 (0.8)28 (2)34 (0.9)47 (2)60 (2)15/15
texp liao noiseless 7.2 (0.8)12 (1)18 (0.8)24 (1)30 (1)43 (1.0)54 (2)15/15

Δ fopt
f2, 40-D
1e1
796
1e0
797
1e-1
799
1e-2
799
1e-3
800
1e-5
802
1e-7
804
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (0.0)★41.5 (0.1)★41.7 (0.1)★41.9 (0.3)★42.1 (0.1)★42.4 (0.2)★42.8 (0.2)★415/15
BIPOP-saACM-k loshchilov noiseless 7.4 (2)8.5 (0.4)9.2 (0.7)10 (0.6)10 (1)11 (0.9)11 (1)15/15
CGA-grid100 holtschulte noiseless 8963 (2e4)2e60/15
CGA-grid16 holtschulte noiseless 617 (210)2820 (1415)2e60/15
CGA-ring100 holtschulte noiseless 287 (92)840 (268)3963 (3324)2e60/15
CGA-ring16 holtschulte noiseless 230 (113)772 (363)3174 (2734)2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 353 (247)980 (398)6917 (1e4)2e60/15
HILL holtschulte noiseless 246 (131)574 (145)5740 (4285)2e60/15
IP-10DDr liao noiseless 58 (4)72 (6)82 (8)89 (5)93 (2)98 (3)100 (2)15/15
IP-500 liao noiseless 58 (6)72 (5)82 (10)89 (6)93 (5)98 (4)100 (2)15/15
IP liao noiseless 58 (3)72 (9)82 (8)89 (7)93 (4)98 (3)100 (2)15/15
MEMPSODE voglis noiseless 8.7 (9)10 (0.1)10 (5)10 (4)10 (0.2)23 (0.8)24 (1)15/15
PRCGA sawyerr noiseless 67 (66)137 (64)306 (109)486 (120)1093 (827)2051 (1157)5252 (2941)4/15
tany liao noiseless 57 (5)71 (4)79 (6)85 (4)89 (5)94 (2)96 (3)15/15
texp liao noiseless 55 (3)66 (6)75 (6)80 (6)84 (8)89 (3)91 (2)15/15

Δ fopt
f3, 40-D
1e1
15526
1e0
15602
1e-1
15612
1e-2
15641
1e-3
15646
1e-5
15651
1e-7
15656
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.23 (0.0)★40.36 (0.1)0.43 (0.1)0.44 (0.1)0.46 (0.1)0.48 (0.1)0.50 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1748 (1682)4e70/15
CGA-grid100 holtschulte noiseless 26 (3)82 (16)2e60/15
CGA-grid16 holtschulte noiseless 4.0 (0.5)13 (3)44 (9)261 (103)2e60/15
CGA-ring100 holtschulte noiseless 5.9 (0.3)11 (0.8)22 (3)50 (6)1909 (1981)2e60/15
CGA-ring16 holtschulte noiseless 1.6 (0.1)4.7 (0.5)14 (2)40 (6)308 (198)2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 3.3 (0.2)8.5 (1)22 (4)63 (19)2e60/15
HILL holtschulte noiseless 1.1 (0.3)3.8 (1.0)13 (2)41 (14)253 (402)2e60/15
IP-10DDr liao noiseless 4e70/15
IP-500 liao noiseless 2753 (2318)4e70/15
IP liao noiseless 4e70/15
MEMPSODE voglis noiseless 35 (17)160 (85)282 (191)282 (105)282 (181)290 (171)290 (181)15/15
PRCGA sawyerr noiseless 3.8 (0.8)13 (14)18 (6)20 (12)43 (19)111 (230)197 (150)9/15
tany liao noiseless 7705 (9855)4e70/15
texp liao noiseless 6590 (1e4)4e70/15

Δ fopt
f4, 40-D
1e1
15536
1e0
15601
1e-1
15659
1e-2
15678
1e-3
15703
1e-5
15733
1e-7
2.8e5
#succ
6/15
BIPOP-aCMA-STEP loshchilov noiseless 0.40 (0.0)0.71 (0.0)1.0 (0.1)1.3 (0.1)1.6 (0.1)1.9 (0.1)0.11 (7e-3)15/15
BIPOP-saACM-k loshchilov noiseless 4e70/15
CGA-grid100 holtschulte noiseless 34 (5)143 (68)2e60/15
CGA-grid16 holtschulte noiseless 5.6 (0.5)19 (3)63 (22)2e60/15
CGA-ring100 holtschulte noiseless 6.8 (0.4)13 (1)26 (3)70 (14)2e60/15
CGA-ring16 holtschulte noiseless 2.2 (0.4)7.1 (2)20 (5)62 (13)1905 (1401)2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 4.4 (0.5)12 (2)35 (7)91 (20)2e60/15
HILL holtschulte noiseless 1.5 (0.3)5.7 (0.7)20 (8)56 (16)2e60/15
IP-10DDr liao noiseless 4e70/15
IP-500 liao noiseless 4e70/15
IP liao noiseless 4e70/15
MEMPSODE voglis noiseless 104 (82)823 (570)2301 (1427)2298 (3333)2703 (3063)2700 (2823)240 (124)1/15
PRCGA sawyerr noiseless 6.6 (1)15 (2)16 (9)16 (9)25 (13)59 (38)10 (10)8/15
tany liao noiseless 4e70/15
texp liao noiseless 4e70/15

Δ fopt
f5, 40-D
1e1
98
1e0
116
1e-1
120
1e-2
121
1e-3
121
1e-5
121
1e-7
121
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 0.84 (0)★40.71 (0)★40.68 (0)★40.68 (0)★40.68 (0)★40.68 (0)★40.68 (0)★415/15
BIPOP-saACM-k loshchilov noiseless 3.1 (0.4)3.0 (0.3)2.9 (0.3)2.9 (0.3)2.9 (0.2)2.9 (0.2)2.9 (0.2)15/15
CGA-grid100 holtschulte noiseless 361 (58)363 (70)371 (62)375 (64)375 (47)375 (58)375 (80)15/15
CGA-grid16 holtschulte noiseless 65 (7)65 (8)67 (8)67 (7)67 (7)67 (8)67 (8)15/15
CGA-ring100 holtschulte noiseless 176 (9)180 (12)190 (12)190 (8)190 (11)190 (16)190 (11)15/15
CGA-ring16 holtschulte noiseless 32 (3)33 (3)35 (3)35 (4)35 (4)35 (3)35 (3)15/15
CMAES Hutter hutter noiseless 4.9 (0.4)4.8 (0.8)4.7 (0.6)4.7 (0.8)4.7 (0.7)4.7 (0.5)4.7 (0.4)15/15
GA-100 holtschulte noiseless 78 (8)84 (4)88 (10)90 (5)90 (5)90 (10)90 (8)15/15
HILL holtschulte noiseless 11 (3)12 (2)12 (2)11 (2)11 (2)11 (2)11 (2)15/15
IP-10DDr liao noiseless 249 (360)266 (110)298 (284)367 (408)504 (520)609 (818)640 (1229)15/15
IP-500 liao noiseless 249 (305)266 (222)298 (307)367 (436)504 (515)609 (519)640 (1229)15/15
IP liao noiseless 249 (557)266 (192)298 (301)367 (502)504 (507)609 (499)640 (812)15/15
MEMPSODE voglis noiseless 6.3 (0.4)6.1 (0.8)6.0 (0.9)6.0 (0.7)6.0 (0.5)6.0 (1)6.0 (0.8)15/15
PRCGA sawyerr noiseless 8.7e4 (1e5)2e60/15
tany liao noiseless 206 (260)238 (269)261 (178)273 (146)306 (248)345 (300)414 (488)15/15
texp liao noiseless 4977 (1e4)1.1e4 (4e4)1.5e4 (431)1.9e4 (4e4)2.3e4 (9e4)3.2e4 (1e5)3.3e4 (6e4)15/15

Δ fopt
f6, 40-D
1e1
3507
1e0
5523
1e-1
7168
1e-2
9470
1e-3
11538
1e-5
15007
1e-7
19222
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.6 (0.3)1.4 (0.1)1.4 (0.1)1.3 (0.1)1.3 (0.1)1.3 (0.1)1.3 (0.1)15/15
BIPOP-saACM-k loshchilov noiseless 1.4 (0.0)1.3 (0.2)1.4 (0.2)1.4 (0.1)1.5 (0.2)1.7 (0.2)1.8 (0.5)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 1042 (718)2e60/15
CGA-ring100 holtschulte noiseless 127 (34)253 (143)2076 (2426)2e60/15
CGA-ring16 holtschulte noiseless 279 (350)2537 (947)2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 80 (77)739 (1108)2e60/15
HILL holtschulte noiseless 597 (999)5195 (3983)2e60/15
IP-10DDr liao noiseless 1.3 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.1)1.2 (0.1)1.3 (0.1)1.3 (0.1)15/15
IP-500 liao noiseless 1.3 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.1)1.2 (0.0)1.3 (0.1)1.3 (0.1)15/15
IP liao noiseless 1.3 (0.2)1.3 (0.1)1.3 (0.0)1.2 (0.1)1.2 (0.1)1.3 (0.1)1.3 (0.1)15/15
MEMPSODE voglis noiseless 20 (9)19 (4)17 (2)15 (5)13 (6)13 (5)31 (47)15/15
PRCGA sawyerr noiseless 3182 (3990)1.1e4 (1e4)4e60/15
tany liao noiseless 1.3 (0.1)1.3 (0.1)1.4 (0.1)1.3 (0.0)1.2 (0.1)1.3 (0.1)1.3 (0.1)15/15
texp liao noiseless 1.3 (0.1)1.4 (0.1)1.4 (0.0)1.4 (0.1)1.4 (0.1)1.5 (0.1)1.6 (0.1)15/15

Δ fopt
f7, 40-D
1e1
10698
1e0
17839
1e-1
41037
1e-2
66294
1e-3
66294
1e-5
66294
1e-7
68145
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.1 (0.9)4.1 (2)2.3 (1.0)1.5 (0.6)1.5 (0.6)1.5 (0.6)1.4 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 1.2 (0.5)1.6 (1.0)0.93 (0.5)0.65 (0.2)0.65 (0.3)0.65 (0.3)0.64 (0.3)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 5.6 (5)40070/15
GA-100 holtschulte noiseless 2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 6.2 (4)10 (7)4.8 (3)3.1 (1)3.1 (1)3.1 (2)3.0 (1)15/15
IP-500 liao noiseless 6.2 (9)10 (5)4.8 (2)3.1 (2)3.1 (1)3.1 (1)3.0 (2)15/15
IP liao noiseless 6.2 (3)10 (7)4.8 (2)3.1 (2)3.1 (2)3.1 (2)3.0 (2)15/15
MEMPSODE voglis noiseless 69 (146)3672 (4524)6861 (1e4)4345 (3548)4345 (8983)4345 (3774)2e70/15
PRCGA sawyerr noiseless 2e60/15
tany liao noiseless 2.1 (1)6.8 (2)3.4 (1.0)2.2 (0.7)2.2 (0.7)2.2 (0.7)2.2 (0.6)15/15
texp liao noiseless 11 (7)87 (126)38 (40)24 (6)24 (23)24 (36)23 (11)15/15

Δ fopt
f8, 40-D
1e1
7080
1e0
10655
1e-1
11012
1e-2
11265
1e-3
11430
1e-5
11701
1e-7
11969
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.6 (0.6)6.0 (0.3)6.1 (8)6.1 (8)6.1 (0.3)6.1 (8)6.1 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 1.6 (0.2)1.5 (0.2)1.5 (0.1)1.5 (0.2)1.5 (0.2)1.5 (0.1)1.5 (0.4)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 1986 (3099)2658 (2346)2e60/15
HILL holtschulte noiseless 612 (506)799 (637)2e60/15
IP-10DDr liao noiseless 7.1 (0.8)7.0 (3)7.1 (0.5)7.2 (5)7.2 (1)7.2 (0.4)7.2 (3)15/15
IP-500 liao noiseless 7.1 (0.7)7.0 (0.3)7.1 (6)7.2 (3)7.2 (0.8)7.2 (3)7.2 (5)15/15
IP liao noiseless 7.1 (0.7)7.0 (0.6)7.1 (3)7.2 (3)7.2 (3)7.2 (3)7.2 (0.9)15/15
MEMPSODE voglis noiseless 19 (9)21 (19)23 (27)23 (5)24 (3)24 (8)28 (16)15/15
PRCGA sawyerr noiseless 1189 (1411)1557 (1016)4e60/15
tany liao noiseless 7.2 (1)6.3 (1)6.5 (2)6.6 (0.8)6.6 (0.7)6.6 (2)6.6 (1)15/15
texp liao noiseless 7.2 (1.0)7.1 (0.2)7.3 (3)7.3 (1.0)7.3 (3)7.3 (0.4)7.3 (5)15/15

Δ fopt
f9, 40-D
1e1
6122
1e0
12982
1e-1
13300
1e-2
13496
1e-3
13651
1e-5
13909
1e-7
14142
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 6.1 (0.3)3.9 (0.2)4.0 (0.2)4.1 (0.1)4.1 (0.2)4.1 (0.2)4.1 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 1.8 (0.3)1.3 (0.4)1.3 (0.2)1.3 (0.4)1.3 (0.7)1.3 (0.3)1.3 (0.7)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 8.6 (0.4)6.9 (4)7.0 (2)7.1 (4)7.1 (4)7.1 (4)7.1 (4)15/15
IP-500 liao noiseless 8.6 (0.9)6.9 (3)7.0 (3)7.1 (4)7.1 (5)7.1 (0.2)7.1 (4)15/15
IP liao noiseless 8.6 (1)6.9 (4)7.0 (4)7.1 (5)7.1 (3)7.1 (2)7.1 (4)15/15
MEMPSODE voglis noiseless 35 (11)30 (30)31 (8)32 (9)32 (23)32 (30)35 (20)15/15
PRCGA sawyerr noiseless 1579 (3029)4e60/15
tany liao noiseless 8.6 (2)6.8 (2)6.9 (4)7.0 (3)7.0 (3)7.1 (2)7.1 (4)15/15
texp liao noiseless 8.3 (0.7)5.9 (4)6.1 (2)6.2 (0.4)6.2 (2)6.2 (0.3)6.2 (0.2)15/15

Δ fopt
f10, 40-D
1e1
25536
1e0
29762
1e-1
35676
1e-2
51579
1e-3
56007
1e-5
65128
1e-7
70824
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.1 (0.0)1.2 (0.1)1.1 (0.0)0.79 (0.0)0.77 (0.0)0.71 (0.0)0.67 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 0.25 (0.0)0.23 (0.0)0.21 (0.0)0.15 (0.0)0.15 (0.0)0.13 (0.0)0.13 (8e-3)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 1.8 (0.2)1.9 (0.2)1.8 (0.2)1.3 (0.1)1.3 (0.1)1.2 (0.0)1.1 (0.0)15/15
IP-500 liao noiseless 1.8 (0.1)1.9 (0.1)1.8 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.0)1.1 (0.0)15/15
IP liao noiseless 1.8 (0.1)1.9 (0.2)1.8 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.1)1.1 (0.0)15/15
MEMPSODE voglis noiseless 2e70/15
PRCGA sawyerr noiseless 4e60/15
tany liao noiseless 1.8 (0.1)1.9 (0.2)1.7 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.0)1.1 (0.0)15/15
texp liao noiseless 1.6 (0.2)1.7 (0.2)1.6 (0.2)1.2 (0.0)1.2 (0.1)1.1 (0.0)1.0 (0.0)15/15

Δ fopt
f11, 40-D
1e1
2368
1e0
4855
1e-1
11681
1e-2
25315
1e-3
29749
1e-5
38949
1e-7
48211
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 5.1 (0.2)2.7 (0.1)1.2 (0.0)0.58 (7e-3)0.51 (0.0)0.43 (4e-3)0.37 (7e-3)15/15
BIPOP-saACM-k loshchilov noiseless 2.8 (2)1.4 (0.8)0.61 (0.3)0.29 (0.1)0.25 (0.1)0.20 (0.1)0.17 (0.1)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 1498 (1091)2e60/15
CGA-ring16 holtschulte noiseless 606 (403)2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 531 (174)2e60/15
HILL holtschulte noiseless 932 (882)2e60/15
IP-10DDr liao noiseless 13 (0.4)6.9 (0.1)3.1 (0.1)1.5 (0.0)1.3 (0.0)1.1 (0.0)0.94 (0.0)15/15
IP-500 liao noiseless 13 (0.4)6.9 (0.1)3.1 (0.1)1.5 (0.0)1.3 (0.0)1.1 (0.0)0.94 (0.0)15/15
IP liao noiseless 13 (0.2)6.9 (0.1)3.1 (0.1)1.5 (0.0)1.3 (0.0)1.1 (0.0)0.94 (9e-3)15/15
MEMPSODE voglis noiseless 0.72 (0.1)★41.2 (1)0.57 (0.7)0.35 (0.4)0.64 (0.5)17 (12)2e70/15
PRCGA sawyerr noiseless 2470 (1896)4e60/15
tany liao noiseless 12 (0.5)6.5 (0.1)2.9 (0.1)1.4 (0.0)1.3 (0.0)1.0 (0.0)0.87 (0.0)15/15
texp liao noiseless 10 (0.4)5.7 (0.1)2.5 (0.1)1.2 (0.0)1.1 (0.0)0.89 (0.0)0.76 (0.0)15/15

Δ fopt
f12, 40-D
1e1
4169
1e0
7452
1e-1
9174
1e-2
10751
1e-3
13146
1e-5
22758
1e-7
25192
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.9 (1)2.2 (1)2.4 (1)2.3 (0.7)2.2 (0.7)1.5 (0.4)1.5 (0.3)15/15
BIPOP-saACM-k loshchilov noiseless 0.34 (0.3)0.54 (0.4)0.72 (0.2)0.74 (0.2)0.73 (0.2)0.55 (0.1)0.57 (0.1)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 7174 (6956)2e60/15
CGA-ring100 holtschulte noiseless 434 (160)2e60/15
CGA-ring16 holtschulte noiseless 629 (505)1988 (1544)2e60/15
CMAES Hutter hutter noiseless 1.4 (1.0)40070/15
GA-100 holtschulte noiseless 710 (744)2e60/15
HILL holtschulte noiseless 539 (628)2e60/15
IP-10DDr liao noiseless 1.1 (1)2.4 (0.8)2.8 (0.4)2.9 (1)2.8 (0.7)2.1 (0.3)2.2 (0.3)15/15
IP-500 liao noiseless 1.1 (1)2.4 (0.8)2.8 (0.8)2.9 (0.7)2.8 (0.9)2.1 (0.8)2.2 (0.5)15/15
IP liao noiseless 1.1 (0.1)2.4 (0.6)2.8 (0.9)2.9 (1)2.8 (0.4)2.1 (0.5)2.2 (0.6)15/15
MEMPSODE voglis noiseless 1.2 (1)1.6 (2)5.0 (2)5.7 (5)7.5 (4)20 (13)253 (361)5/15
PRCGA sawyerr noiseless 386 (258)598 (1212)2624 (3451)4846 (7856)4e60/15
tany liao noiseless 1.6 (1)2.2 (2)2.8 (1)2.9 (1)2.8 (1)2.1 (0.5)2.2 (0.6)15/15
texp liao noiseless 1.4 (0.0)2.0 (1)2.5 (2)2.7 (1)2.6 (0.6)2.0 (0.7)2.1 (0.5)15/15

Δ fopt
f13, 40-D
1e1
2029
1e0
6916
1e-1
8734
1e-2
11861
1e-3
71936
1e-5
98467
1e-7
1.2e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.6 (0.1)2.2 (1)3.9 (4)6.3 (4)1.4 (1)1.8 (1)2.6 (1)15/15
BIPOP-saACM-k loshchilov noiseless 0.77 (0.6)0.55 (0.3)0.94 (0.8)2.0 (2)0.59 (0.4)0.72 (0.5)0.68 (0.8)15/15
CGA-grid100 holtschulte noiseless 1.5e4 (2e4)2e60/15
CGA-grid16 holtschulte noiseless 463 (500)2e60/15
CGA-ring100 holtschulte noiseless 212 (82)798 (1172)2e60/15
CGA-ring16 holtschulte noiseless 1196 (3224)1326 (1591)2e60/15
CMAES Hutter hutter noiseless 2.1 (1)8.7 (13)40070/15
GA-100 holtschulte noiseless 505 (1287)2e60/15
HILL holtschulte noiseless 585 (499)939 (452)2e60/15
IP-10DDr liao noiseless 3.1 (4)2.9 (3)7.6 (9)9.3 (8)2.4 (0.8)2.5 (0.8)2.4 (0.6)15/15
IP-500 liao noiseless 3.1 (4)2.9 (5)7.6 (12)9.3 (7)2.4 (1)2.5 (0.7)2.4 (0.8)15/15
IP liao noiseless 3.1 (4)2.9 (2)7.6 (7)9.3 (7)2.4 (0.8)2.5 (0.9)2.4 (0.6)15/15
MEMPSODE voglis noiseless 1.4 (1)1.1 (1)1.5 (0.5)2.7 (1)1.8 (1)44 (62)408 (250)0/15
PRCGA sawyerr noiseless 769 (991)1227 (1143)3064 (3435)4846 (3878)4e60/15
tany liao noiseless 2.6 (4)3.6 (5)8.1 (9)7.9 (5)1.9 (1)2.4 (0.5)2.5 (0.7)15/15
texp liao noiseless 1.5 (0.1)3.7 (3)8.0 (7)11 (7)2.2 (1.0)2.1 (1)2.6 (0.3)15/15

Δ fopt
f14, 40-D
1e1
304
1e0
616
1e-1
777
1e-2
1105
1e-3
2207
1e-5
4825
1e-7
57711
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 3.6 (0.9)2.9 (0.2)3.4 (0.3)4.0 (0.3)3.6 (0.4)4.0 (0.3)0.60 (0.0)15/15
BIPOP-saACM-k loshchilov noiseless 2.1 (0.5)1.5 (0.2)1.5 (0.2)1.9 (0.2)1.4 (0.1)★41.2 (0.0)0.15 (8e-3)15/15
CGA-grid100 holtschulte noiseless 87 (21)118 (22)315 (55)2e60/15
CGA-grid16 holtschulte noiseless 15 (4)20 (3)51 (12)1459 (466)2e60/15
CGA-ring100 holtschulte noiseless 44 (6)62 (7)121 (15)740 (76)2e60/15
CGA-ring16 holtschulte noiseless 9.1 (2)11 (2)25 (3)433 (150)2e60/15
CMAES Hutter hutter noiseless 2.5 (0.3)2.4 (0.2)3.0 (0.3)5.9 (3)40070/15
GA-100 holtschulte noiseless 17 (3)24 (3)56 (9)655 (290)2e60/15
HILL holtschulte noiseless 2.9 (0.4)3.5 (0.7)12 (3)346 (117)2e60/15
IP-10DDr liao noiseless 2.2 (0.4)2.2 (0.2)2.8 (0.2)3.8 (0.3)4.5 (0.2)7.0 (0.4)1.2 (0.0)15/15
IP-500 liao noiseless 2.2 (0.5)2.2 (0.3)2.8 (0.2)3.8 (0.3)4.5 (0.2)7.0 (0.5)1.2 (0.1)15/15
IP liao noiseless 2.2 (0.3)2.2 (0.2)2.8 (0.2)3.8 (0.4)4.5 (0.4)7.0 (0.7)1.2 (0.1)15/15
MEMPSODE voglis noiseless 1.3 (0.4)1.1 (0.2)★31.2 (0.2)1.9 (0.6)8.2 (5)13 (11)2e70/15
PRCGA sawyerr noiseless 8.2 (0.9)13 (2)26 (8)156 (106)2279 (1006)4e60/15
tany liao noiseless 2.1 (0.3)2.2 (0.3)2.9 (0.2)3.9 (0.3)4.7 (0.2)6.8 (0.5)1.1 (0.0)15/15
texp liao noiseless 1.4 (0.2)1.9 (0.2)2.6 (0.2)3.6 (0.4)4.2 (0.3)6.1 (0.3)1.00 (0.1)15/15

Δ fopt
f15, 40-D
1e1
1.9e5
1e0
7.9e5
1e-1
1.0e6
1e-2
1.1e6
1e-3
1.1e6
1e-5
1.1e6
1e-7
1.1e6
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.0 (0.4)1.0 (0.3)1.1 (0.3)1.1 (0.3)1.1 (0.3)1.1 (0.3)1.1 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 0.81 (0.4)0.94 (0.4)1.1 (0.1)1.1 (0.4)1.1 (0.1)1.1 (0.6)1.1 (0.2)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 0.82 (0.3)0.74 (0.2)0.66 (0.2)0.67 (0.1)0.68 (0.1)0.69 (0.0)0.70 (0.2)15/15
IP-500 liao noiseless 0.82 (0.3)0.81 (0.4)1.2 (1)1.2 (0.7)1.2 (0.7)1.2 (0.7)1.2 (0.8)15/15
IP liao noiseless 0.82 (0.2)0.74 (0.3)0.66 (0.2)0.67 (0.1)0.68 (0.2)0.69 (0.1)0.70 (0.2)15/15
MEMPSODE voglis noiseless 2e70/15
PRCGA sawyerr noiseless 4e60/15
tany liao noiseless 0.84 (0.3)0.71 (0.1)0.66 (0.2)0.66 (0.2)0.67 (0.2)0.68 (0.2)0.69 (0.1)15/15
texp liao noiseless 0.67 (0.4)0.55 (0.2)0.56 (0.3)0.57 (0.3)0.58 (0.3)0.60 (0.2)0.62 (0.0)15/15

Δ fopt
f16, 40-D
1e1
5244
1e0
72122
1e-1
3.2e5
1e-2
7.1e5
1e-3
1.4e6
1e-5
2.0e6
1e-7
2.0e6
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.0 (0.3)1.2 (0.6)0.76 (0.4)0.56 (0.3)0.56 (0.4)0.53 (0.3)0.53 (0.2)15/15
BIPOP-saACM-k loshchilov noiseless 0.94 (0.4)0.61 (0.2)0.57 (0.4)0.68 (0.5)0.42 (0.3)0.53 (0.4)0.58 (0.3)15/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 5566 (6102)2e60/15
CGA-ring100 holtschulte noiseless 37 (47)2e60/15
CGA-ring16 holtschulte noiseless 1058 (2860)2e60/15
CMAES Hutter hutter noiseless 3.7 (3)40070/15
GA-100 holtschulte noiseless 339 (763)2e60/15
HILL holtschulte noiseless 5611 (4291)2e60/15
IP-10DDr liao noiseless 0.55 (0.1)0.20 (0.2)0.34 (0.2)0.37 (0.1)0.30 (0.2)0.32 (0.1)0.35 (0.0)15/15
IP-500 liao noiseless 0.55 (0.1)0.20 (0.2)0.34 (0.2)0.37 (0.2)0.30 (0.1)0.30 (0.2)0.34 (0.1)15/15
IP liao noiseless 0.55 (0.1)0.20 (0.2)0.34 (0.2)0.37 (0.1)0.30 (0.2)0.32 (0.1)0.35 (0.1)15/15
MEMPSODE voglis noiseless 7.5 (10)2e70/15
PRCGA sawyerr noiseless 120 (382)4e60/15
tany liao noiseless 0.58 (0.1)0.11 (0.0)0.24 (0.2)0.36 (0.2)0.29 (0.3)0.27 (0.1)0.28 (0.1)15/15
texp liao noiseless 0.45 (0.1)0.22 (0.2)0.27 (0.1)0.25 (0.1)0.22 (0.1)0.20 (0.1)0.20 (0.1)15/15

Δ fopt
f17, 40-D
1e1
399
1e0
4220
1e-1
14158
1e-2
34948
1e-3
51958
1e-5
1.3e5
1e-7
2.7e5
#succ
14/15
BIPOP-aCMA-STEP loshchilov noiseless 1.7 (0.5)0.54 (0.1)1.0 (1)1.1 (0.1)1.1 (0.3)0.97 (0.6)0.99 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 0.99 (0.4)2.4 (7)8.4 (4)3.6 (1)2.8 (0.6)1.6 (0.6)1.1 (0.4)15/15
CGA-grid100 holtschulte noiseless 1550 (158)2e60/15
CGA-grid16 holtschulte noiseless 976 (2509)2e60/15
CGA-ring100 holtschulte noiseless 11 (2)2e60/15
CGA-ring16 holtschulte noiseless 3.8 (1)2e60/15
CMAES Hutter hutter noiseless 1.0 (0.6)0.59 (0.2)1.0 (0.3)40070/15
GA-100 holtschulte noiseless 3.3 (1)717 (831)2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 0.81 (0.3)0.49 (0.1)0.95 (0.9)1.1 (0.1)1.1 (0.3)1.1 (0.7)0.92 (0.3)15/15
IP-500 liao noiseless 0.81 (0.1)0.49 (0.1)0.95 (1.0)1.1 (0.3)1.1 (0.3)1.1 (0.2)0.92 (0.3)15/15
IP liao noiseless 0.81 (0.2)0.49 (0.3)0.95 (1)1.1 (0.3)1.1 (0.2)1.1 (0.7)0.92 (0.3)15/15
MEMPSODE voglis noiseless 27 (15)279 (59)9316 (2e4)8136 (1e4)2e70/15
PRCGA sawyerr noiseless 1.5 (1)1400 (1422)4e60/15
tany liao noiseless 0.59 (0.1)0.43 (0.1)0.47 (0.4)0.58 (0.4)0.75 (0.3)0.90 (0.5)0.76 (0.4)15/15
texp liao noiseless 0.31 (0.1)★20.46 (0.1)0.92 (0.8)0.84 (0.5)0.86 (0.5)1.1 (0.6)0.78 (0.4)15/15

Δ fopt
f18, 40-D
1e1
1442
1e0
16998
1e-1
47068
1e-2
1.3e5
1e-3
1.9e5
1e-5
6.7e5
1e-7
9.5e5
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.0 (0.2)0.50 (0.9)0.94 (0.4)0.74 (0.5)0.89 (0.6)0.69 (0.6)0.68 (0.5)15/15
BIPOP-saACM-k loshchilov noiseless 0.84 (0.3)3.3 (4)3.1 (2)1.6 (0.7)1.4 (0.7)0.90 (1)0.83 (0.7)14/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 9058 (6241)2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 1.0 (0.5)0.48 (0.2)40070/15
GA-100 holtschulte noiseless 108 (1)2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 0.81 (0.2)0.38 (0.0)1.1 (0.7)0.72 (0.3)0.93 (0.4)0.90 (0.5)0.84 (1)15/15
IP-500 liao noiseless 0.81 (0.2)0.38 (0.1)1.1 (0.5)0.72 (0.3)0.93 (0.4)0.97 (1)0.82 (0.6)15/15
IP liao noiseless 0.81 (0.2)0.38 (0.5)1.1 (0.6)0.72 (0.3)0.93 (0.3)0.90 (0.5)0.84 (0.3)15/15
MEMPSODE voglis noiseless 207 (117)1866 (2680)2e70/15
PRCGA sawyerr noiseless 3.9 (1.0)4e60/15
tany liao noiseless 0.79 (0.1)0.31 (0.0)0.86 (0.6)0.66 (0.2)0.69 (0.2)0.61 (0.3)0.57 (0.3)15/15
texp liao noiseless 0.70 (0.1)0.62 (0.8)0.75 (0.3)0.57 (0.7)0.67 (0.5)0.55 (1e-2)0.45 (0.3)15/15

Δ fopt
f19, 40-D
1e1
1
1e0
1
1e-1
1.4e6
1e-2
1.7e7
1e-3
2.6e7
1e-5
4.5e7
1e-7
4.5e7
#succ
8/15
BIPOP-aCMA-STEP loshchilov noiseless 667 (77)6.6e4 (4e4)1.0 (0.7)0.97 (0.8)1.3 (1.0)1.2 (1)1.2 (1)8/15
BIPOP-saACM-k loshchilov noiseless 322 (86)6.7e4 (5e4)0.75 (1.0)1.1 (0.5)1.2 (1)1.5 (1)1.5 (2)7/15
CGA-grid100 holtschulte noiseless 1.2e5 (7e4)2e60/15
CGA-grid16 holtschulte noiseless 3.0e5 (5e4)2e60/15
CGA-ring100 holtschulte noiseless 8853 (3761)2e60/15
CGA-ring16 holtschulte noiseless 3831 (3642)2e60/15
CMAES Hutter hutter noiseless 419 (36)40070/15
GA-100 holtschulte noiseless 2508 (603)2e60/15
HILL holtschulte noiseless 2.3e5 (2e6)2e60/15
IP-10DDr liao noiseless 398 (312)1.4e5 (5e4)2.8 (3)0.74 (0.2)0.60 (0.2)0.35 (0.1)0.35 (0.1)15/15
IP-500 liao noiseless 398 (318)1.4e5 (5e4)2.8 (4)16 (19)4e70/15
IP liao noiseless 398 (300)1.4e5 (2e4)2.8 (5)0.74 (0.4)0.60 (0.2)0.35 (0.1)0.35 (0.2)15/15
MEMPSODE voglis noiseless 1.1e4 (4708)5.9e7 (8e7)2e70/15
PRCGA sawyerr noiseless 207 (11)715 (596)★40.77 (0.2)4e60/15
tany liao noiseless 306 (173)5.7e5 (1e4)3.4 (5)0.72 (0.5)0.55 (0.4)0.35 (0.2)0.35 (0.2)15/15
texp liao noiseless 7.1 (6)6.7e5 (4e6)1.6 (2)0.53 (0.1)0.42 (0.1)0.24 (0.2)0.25 (0.2)15/15

Δ fopt
f20, 40-D
1e1
222
1e0
1.3e5
1e-1
1.6e8
1e-2
1e-3
1e-5
1e-7
#succ
0/15
BIPOP-aCMA-STEP loshchilov noiseless 5.1 (0.7)8.0 (4)0.41 (0.3)    0/15
BIPOP-saACM-k loshchilov noiseless 2.3 (0.6)9.1 (3)0.81 (0.3)    0/15
CGA-grid100 holtschulte noiseless 141 (22)2.0 (1)    0/15
CGA-grid16 holtschulte noiseless 23 (6)0.35 (0.2)    0/15
CGA-ring100 holtschulte noiseless 68 (6)0.48 (0.1)    0/15
CGA-ring16 holtschulte noiseless 13 (2)0.12 (0.0)    0/15
CMAES Hutter hutter noiseless 3.9 (0.6)    0/15
GA-100 holtschulte noiseless 31 (6)0.27 (0.1)    0/15
HILL holtschulte noiseless 6.2 (2)0.08 (0.0)    0/15
IP-10DDr liao noiseless 4.2 (0.4)16 (3)0.14 (0.1)3.5e7 (2e7) 3.5e7 (4e7) 3.5e7 (3e7) 3.5e7 (3e7) 12/15
IP-500 liao noiseless 4.2 (0.4)1377 (1272)    0/15
IP liao noiseless 4.2 (0.3)16 (4)0.14 (0.0)3.5e7 (3e7) 3.5e7 (4e7) 3.5e7 (2e7) 3.5e7 (2e7) 12/15
MEMPSODE voglis noiseless 1.6 (0.3)1.3 (0.7)    0/15
PRCGA sawyerr noiseless 10 (1)7.3 (7)    0/15
tany liao noiseless 4.1 (0.6)20 (10)0.16 (6e-3)1.4e8 (1e8) 1.4e8 (1e8) 1.4e8 (1e8) 1.4e8 (2e8) 4/15
texp liao noiseless 2.1 (0.5)52 (23)    0/15

Δ fopt
f21, 40-D
1e1
1044
1e0
21144
1e-1
1.0e5
1e-2
1.0e5
1e-3
1.0e5
1e-5
1.0e5
1e-7
1.0e5
#succ
26/30
BIPOP-aCMA-STEP loshchilov noiseless 3.5 (5)151 (386)86 (378)86 (127)86 (139)85 (126)85 (176)14/15
BIPOP-saACM-k loshchilov noiseless 1.7 (2)40 (128)30 (14)30 (54)30 (53)30 (53)30 (52)15/15
CGA-grid100 holtschulte noiseless 741 (974)621 (378)2e60/15
CGA-grid16 holtschulte noiseless 483 (957)1326 (1159)2e60/15
CGA-ring100 holtschulte noiseless 15 (3)145 (235)56 (99)56 (79)57 (114)59 (118)64 (122)4/15
CGA-ring16 holtschulte noiseless 3.6 (1)261 (284)55 (65)55 (35)55 (20)55 (79)58 (103)4/15
CMAES Hutter hutter noiseless 2.7 (2)2.7 (2)0.57 (0.5)0.57 (0.9)0.58 (0.6)0.58 (0.6)0.58 (0.8)1/15
GA-100 holtschulte noiseless 303 (480)379 (331)129 (328)129 (223)129 (114)131 (79)135 (209)2/15
HILL holtschulte noiseless 1279 (2396)379 (544)2e60/15
IP-10DDr liao noiseless 2.2 (6)1238 (2311)1723 (1004)1718 (2724)1713 (2058)1703 (2893)1695 (966)3/15
IP-500 liao noiseless 2.2 (11)3785 (4730)4e70/15
IP liao noiseless 2.2 (6)2931 (3311)4e70/15
MEMPSODE voglis noiseless 2.3 (0.4)40 (83)22 (10)22 (7)22 (20)22 (7)43 (54)12/15
PRCGA sawyerr noiseless 272 (711)424 (483)204 (164)203 (468)203 (131)203 (224)203 (183)2/15
tany liao noiseless 0.71 (0.1)390 (277)667 (1163)665 (1654)663 (446)659 (843)657 (860)6/15
texp liao noiseless 1.1 (2)109 (284)60 (61)60 (84)60 (92)60 (39)59 (63)15/15

Δ fopt
f22, 40-D
1e1
3090
1e0
35442
1e-1
6.5e5
1e-2
6.5e5
1e-3
6.5e5
1e-5
6.5e5
1e-7
6.5e5
#succ
8/30
BIPOP-aCMA-STEP loshchilov noiseless 7.8 (16)391 (1060)218 (274)218 (298)218 (117)217 (96)216 (210)4/15
BIPOP-saACM-k loshchilov noiseless 7.2 (45)430 (721)250 (200)249 (295)249 (187)248 (366)248 (262)3/15
CGA-grid100 holtschulte noiseless 574 (324)115 (71)2e60/15
CGA-grid16 holtschulte noiseless 742 (1133)790 (240)2e60/15
CGA-ring100 holtschulte noiseless 5.4 (2)39 (42)2e60/15
CGA-ring16 holtschulte noiseless 163 (162)226 (508)2e60/15
CMAES Hutter hutter noiseless 0.62 (0.4)0.49 (0.5)40070/15
GA-100 holtschulte noiseless 49 (162)113 (113)2e60/15
HILL holtschulte noiseless 740 (1618)226 (240)2e60/15
IP-10DDr liao noiseless 388 (995)1290 (3104)4e70/15
IP-500 liao noiseless 3262 (9712)1290 (1693)4e70/15
IP liao noiseless 1109 (7)1290 (847)4e70/15
MEMPSODE voglis noiseless 0.77 (0.9)50 (145)98 (178)98 (60)98 (108)97 (94)445 (344)0/15
PRCGA sawyerr noiseless 274 (648)382 (340)3e60/15
tany liao noiseless 87 (446)1017 (340)4e70/15
texp liao noiseless 158 (436)477 (713)4e70/15

Δ fopt
f23, 40-D
1e1
7.0
1e0
11925
1e-1
75453
1e-2
6.6e5
1e-3
1.3e6
1e-5
3.2e6
1e-7
3.4e6
#succ
15/15
BIPOP-aCMA-STEP loshchilov noiseless 1.3 (1)9.4 (3)1.9 (3)1.1 (2)1.7 (1)0.81 (0.6)1.00 (0.8)15/15
BIPOP-saACM-k loshchilov noiseless 4.7 (2)8.9 (11)1.5 (2)1.3 (0.9)1.5 (1)1.1 (0.4)1.1 (1)15/15
CGA-grid100 holtschulte noiseless 0.96 (0.6)2e60/15
CGA-grid16 holtschulte noiseless 1.1 (0.8)1150 (1614)2e60/15
CGA-ring100 holtschulte noiseless 1.2 (2)163 (173)2e60/15
CGA-ring16 holtschulte noiseless 1.2 (0.6)1109 (1336)2e60/15
CMAES Hutter hutter noiseless 5.4 (9)40070/15
GA-100 holtschulte noiseless 1.4 (2)2386 (5031)2e60/15
HILL holtschulte noiseless 1.4 (1)727 (657)2e60/15
IP-10DDr liao noiseless 1.1 (2)20 (14)3.4 (9)24 (20)442 (399)4e70/15
IP-500 liao noiseless 1.1 (2)20 (52)3.4 (3)19 (22)86 (85)4e70/15
IP liao noiseless 1.1 (0.6)20 (9)3.4 (16)24 (34)442 (493)4e70/15
MEMPSODE voglis noiseless 77 (108)12 (9)2e70/15
PRCGA sawyerr noiseless 0.89 (0.8)3001 (4210)3e60/15
tany liao noiseless 0.78 (0.2)11 (0.7)1.9 (4)27 (25)141 (110)179 (145)173 (173)1/15
texp liao noiseless 1.4 (1)21 (23)8.0 (11)70 (120)4e70/15

Δ fopt
f24, 40-D
1e1
5.8e6
1e0
9.8e7
1e-1
3.0e8
1e-2
3.0e8
1e-3
3.0e8
1e-5
3.0e8
1e-7
3.0e8
#succ
1/15
BIPOP-aCMA-STEP loshchilov noiseless 2.6 (1)0.87 (1.0)1.9 (3)1.9 (1)1.9 (1)1.9 (0.9)1.9 (2)1/15
BIPOP-saACM-k loshchilov noiseless 2.4 (3)0.44 (0.4)4e70/15
CGA-grid100 holtschulte noiseless 2e60/15
CGA-grid16 holtschulte noiseless 2e60/15
CGA-ring100 holtschulte noiseless 2e60/15
CGA-ring16 holtschulte noiseless 2e60/15
CMAES Hutter hutter noiseless 40070/15
GA-100 holtschulte noiseless 2e60/15
HILL holtschulte noiseless 2e60/15
IP-10DDr liao noiseless 4e70/15
IP-500 liao noiseless 4e70/15
IP liao noiseless 4e70/15
MEMPSODE voglis noiseless 2e70/15
PRCGA sawyerr noiseless 4e60/15
tany liao noiseless 47 (31)2.8 (4)1.9 (3)1.9 (1)1.9 (3)1.9 (1)1.9 (1.0)1/15
texp liao noiseless 2.4 (2)0.31 (0.3)4e70/15

Average runtime (aRT in number of function evaluations) divided by the respective best aRT measured during BBOB-2009 in different dimensions. The aRT and in braces, as dispersion measure, the half difference between 10 and 90%-tile of bootstrapped run lengths appear for each algorithm and target, the corresponding reference aRT  in the first row. The different target ∆f-values are shown in the top row. #succ is the number of trials that reached the (final) target fopt+ 10−8. The median number of conducted function evaluations is additionally given in italics, if the target in the last column was never reached. Entries, succeeded by a star, are statistically significantly better (according to the rank-sum test) when compared to all other algorithms of the table, with p = 0.05 or p = 10−k when the number k following the star is larger than 1, with Bonferroni correction by the number of functions (24). A ↓ indicates the same tested against the best algorithm from BBOB 2009. Best results are printed in bold.
Data produced with COCO v2.0.761